Topic: induction list of topics
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50 items are filed under this topic.

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	Fibonacci and induction		2010-07-12
		From James: I'm trying to prove by induction that F(n) <= 2^(n-1) where f(1)=f(2)=1 and f(k)=f(k-1)+f(k-2) for k >=3 is the Fibonacci sequence Answered by Stephen La Rocque and Tyler Wood.
	A proof by induction		2010-03-25
		From SAMUEL: use mathematical induction to proof that each statement is true for every positve integer n 1/1.2+1/2.3+1/3.4+......1/n(n+1)=n/n+1 Answered by Robert Dawson.
	The nth derivative of x^(n-1) log x		2010-03-10
		From shambodeb: This is a successive differentiation problem by Leibnitz theorem If y = xn-1 log x ; Proof nth derivative y(n) = (n-1)!/x Answered by Harley Weston.
	1^3 + 2^3 + 3^3 +4^3 ... n^3 = ?		2010-01-29
		From ireimaima: Hi.. Can u please help me with this question.. I find that when i test eg: n=2 for n (n+1) /4, it seems that it does not giving me the right answer of 1^3 + 2^3 = 9 but 3/2... i'm confuse..can u please help me..thanks so much Prove that: 1^3 + 2^3 + 3^3 +4^3………………………………..n^3 = n (n+1) /4 Answered by Penny Nom.
	A proof by induction		2010-01-12
		From Bhavya: Prove by induction that if Xi >= 0 for all i, then (Summation Xi from 1 to n)^2 >= Summation Xi^2 from 1 to n Answered by Penny Nom.
	Prove by induction		2009-10-02
		From Anonymous: How can you prove the following by induction: Any fraction (A / B), where 0 < (A / B) < 1, can be expressed as a finite sum (1 / c(1)) + (1 / c(2)) + (1 / c(3)) + ... + (1 / c(k)), where c(1), c(2), ..., c(k) are natural numbers greater than 0. [ex. (20 / 99) = (1 / 9) + (1 / 11)] Answered by Claude Tardif.
	Selecting 3 people from 4		2009-06-02
		From muhammadibeaheem: Use mathematical induction to prove that for all integers n≥1, is divisible by 3. Question 2; A club consists of four members.How many sample points are in the sample space when three officers; president, secretary and treasurer, are to be chosen? Answered by Penny Nom.
	Mathematical induction		2008-09-05
		From James: I need to prove a problem by induction regarding the Triangle Inequality. The problem is abs(a1 + a2 +...+an) <= abs(a1) + abs(a2) +...+ abs(an). Answered by Victoria West.
	Mathematical induction		2008-07-11
		From lyn: can you give me a basic example of a mathematical induction Answered by Harley Weston.
	The sum of the digits of a number		2008-06-23
		From Ben: Question: Using mathematical induction, prove that if the sum of the digits of a number is divisible by three, then the number itself is also divisible by 3. Answered by Penny Nom.
	n^3/3 + n^5/5 + 7n/15 is an integer		2008-03-17
		From John: Prove: For all n in Natural Numbers ( n > 1 ), n^3/3 + n^5/5 + 7n/15 is an integer Answered by Stephen La Rocque.
	2^n > n^2 for n> 4 where n is a natural number		2008-03-17
		From John: I've been asked to prove this: 2^n > n^2 for n> 4 and n is a natural number Answered by Penny Nom.
	Induction		2008-03-14
		From Marcelo: Prove by the principle of the math induction that: 1.3.5.7....(2n-1) = (2n)!/(2^n)n! Answered by Harley Weston.
	1/(1x2)+1/(2x3)+1/(3x4)...+1/(n(n+1))		2008-02-20
		From hossun: Find a formula for 1/(1x2)+1/(2x3)+1/(3x4)...+1/(n(n+1)) by examining the values of this expression for small values of n. Use mathematical induction to prove your result. Answered by Stephen La Rocque.
	The Principle of Mathematical Induction		2007-12-15
		From iris: we have some confusion in our problem. Please help us. We would like to know "the principle of mathematical induction" (i) for n=1, p(1) is true. (ii) assume that for n=k>=1, p(k) is true we have to prove p(k+1) is true. Here (Is n=k>=1 true? or Is n=k.1 true?) Thanks. Answered by Penny Nom and Victoria West.
	Mathematical induction		2007-11-27
		From Angels: Please help! Prove the formula for every positive integer 1^3+2^3+3^3+4^3+...+n^3=n^2((n+1)^2/4) Answered by Harley Weston.
	A faulty induction argument		2007-10-31
		From snehal: Find the problem in the following argument. Try to give another example that illustrates the same problem. Claim: All Fibonacci numbers are even. Proof: We will use strong induction. Let P(n) be the proposition that Fn is even. Base case: F0 = 0 is even, so P(0) is true. Inductive step: Assume P(0); : : : ; P(n - 1) to prove P(n): Now Fn = Fn-1 + Fn-2 and Fn-1 and Fn-2 are both even by assumptions P(n - 1) and P(n - 2); so Fn is also even. By induction, all Fibonacci numbers are even. Answered by Stephen La Rocque and Claude Tardif.
	Subsets of a set		2007-10-30
		From Snehal: 1. Let an denote the number of subsets of f{1,2, 3.... n}including the empty set and the set itself.) a) Show an = 2an-1 b) Guess a formula for the value of an and use induction to prove you are right Answered by Stephen La Rocque.
	Induction problem (divisible by 11)		2007-08-29
		From James: Show that 27 * (23 ^ n) + 17 * (10 )^ (2n) is divisible by 11 for all positive integers n. Answered by Stephen La Rocque and Penny Nom.
	Mathematical induction		2007-03-02
		From Suud: Hello sir/ madam I am really confused about this topic, and i am unable to understand it well. So please help me! I need to send me, clear, detailed and main notes about the principle of mathematical Induction, proofs, and applications. And I would be pleased if you sent me, some solved problems for more clarification and understanding. I would like to appreciate your help! Thank You! Answered by Haley Ess.
	cos(n)pi = (-1)^n		2006-12-14
		From Idrees: How can I prove the following: cos(n)pi = (-1)^n Answered by Steve La Rocque.
	The proof of inequality by mathematical induction		2006-12-07
		From Carol: S(n) = 2^n > 10n+7 and n>=10 Answered by Stephen La Rocque.
	The Fibonacci sequence		2006-11-21
		From Ross: Let f0 = 0; f1 = 1,... be the Fibonacci sequence where for all n greater than or equal to 2 fn = fn-1 + fn-2. Let Q = (1+square root of 5)/2. Show that for all positive n greater than or equal to 0, fn less than or equal to Q^(n-1). Answered by Penny Nom.
	Composition of functions		2006-11-19
		From RJ: Let f0(x) = 2/2-x and fn+1 = f0 o fn for n greater than or equal to 0. Find a formula for fn and prove it by mathematical induction. Recall that o represents function composition. i.e., (f o g)(x) = f(g(x)). Answered by Stephen La Rocque.
	Induction		2006-11-16
		From John: Find a formula for 1/(1x3)+1/(2x4)+1/(3x5)...+1/(n(n+2)) by examining the values of this expression for small values of n. Use mathematical induction to prove your result. Answered by Penny Nom.
	A proof by induction		2006-11-06
		From Zamira: i have a problem with this mathematical induction: (1^5)+(2^5)+(3^5)+...+(n^5) = ((n^2)*((n+1)^2)*((2n^2)+2n-1))/12 Answered by Penny Nom.
	Induction		2006-10-31
		From Ross: Suppose that A and B are square matrices with the property AB= BA. Show that AB^n = B^n A for every positive integer n. Answered by Stephen La Rocque and Penny Nom.
	A proof by induction		2006-10-02
		From Zamira: i'm studying induction but i don't get how to proof that 1+2+2^2+2^3+...+2^(n-1) = (2^n) - 1. Answered by Penny Nom.
	Proof by induction		2006-04-24
		From Meshaal: Find an expression for: 1-3+5 - 7 + 9 - 11 + ... + (-1)^(n-1) * (2n-1) and prove that it is correct. Answered by Stephen La Rocque.
	Proving a summation formula by induction		2006-04-19
		From Sharon: Prove by induction that the sum of all values 2^i from i=1 to n equals 2^(n+1) - 2 for n > 1. Answered by Stephen La Rocque.
	A proof by induction		2006-04-09
		From Sharon: prove by induction: For every n>1, show that 2 + 7 + 12 + ...+ (5n-3) = n(5n-1)/2 Answered by Penny Nom.
	Proof by induction		2006-02-10
		From Victoria: how do i prove by induction on n that n Σ 1/i(i+1) = n/(n+1) i=1 for all positive integers n Answered by Penny Nom.
	Proof by induction?		2005-08-10
		From Peter: I am a lecturer and am having a problem with the following Proof by Induction. If (N x N x N x N) + (4 x N x N x N) + (3 x N x N) + (N) = -4000 Prove that N is even! Answered by Chris Fisher and Penny Nom.
	Proof by induction		2004-11-20
		From Vic: Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows: a(1) = 3 and a(k+1) = 2a(k) for k -> 1. Note: Quantities in brackets are subscripts -> means 'equal to or greater than'. Using the recursive formula, the first 4 terms are; a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24 The nth term a(n) = 2n-1 x 3 (equation 1) Equation 1 must be proven using mathematical induction. This is where I am having a problem. Answered by Penny Nom.
	n! > n^2		2004-03-30
		From Jose: How can you prove by mathematical induction that: n! > n2. Answered by Penny Nom.
	Proof by induction		2004-03-02
		From Chris: I need some help of how to solve the problem "use the principle of mathematical induction to prove that the following are true for all positive integers" cos(n x pi + X) = (-1)^n cosX any help would be appreciated Answered by Penny Nom.
	A functional equation		2002-10-14
		From Rob: Let f be a function whose domain is a set of all positive integers and whose range is a subset of the set of all positive integers with these conditions: a) f(n+1)>f(n) b) f(f(n))=3(n) Answered by Claude Tardif.
	Proof by induction		2002-09-26
		From Pooh: Use induction to show that 1 2 + 2 2 + .....+n 2 = (n 3)/3 + (n 2)/2 + n/6 Answered by Paul Betts.
	Proof by induction		2002-08-31
		From Tabius: Use mathematical induction to prove that the following formulae are true for all positive integers: a) 1 + 3 + 5+...+(2n - 1) = n 2 b) 2 n > n. Answered by Penny Nom.
	Proof by induction		2002-02-20
		From Tamaswati: How do I prove the assertion that "the determinant of an upper triangular matrix is the product of the diagonal entries" by mathematical induction? (Before I check this assertion for a few values of n how do I rephrase the assertion slightly so that n appears explicitly in the assertion?) Answered by Penny Nom.
	Proof by induction		2001-10-16
		From John: Can you help me with any of these? For any natural number n > 1, prove that (4n) / (n + 1) < [(2n)!] / [(n!)2]. For any natural number n > 1, prove that 1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(n) > sqrt(n). For any natural number n and any x > 0, prove that xn + xn - 2 + xn - 4 + ... + x-n >= n + 1. Answered by Penny Nom.
	Proof by induction		2001-09-30
		From Kyle: I'm trying to learn induction and I need to see how this done please help with this problem... 20 + 21 + 22 +... + 2n = 2n+1 -1 is true whenever n is a positive integer. Answered by Penny Nom.
	Harmonic numbers		2001-05-23
		From Leslie: The harmonic numbers Hk, k = 1,2,3.....are defined by Hk = 1 + 1/2 + 1/3....1/k I am trying to prove by mathematical induction: H2n >= 1 + n/2 , whenever n is a nonnegative integer. H8 = H23 >= 1 + 3/2 Can you help? Answered by Harley Weston.
	A sequence of even terms		2001-04-29
		From A student: A sequence c is defined recursively as follows: c0 = 2 c1 = 4 c2 = 6 ck= 5ck-3 for all integers Prove that cn is even for all integers. Answered by Leeanne Boehm and Penny Nom.
	Induction		2000-09-07
		From Joe Peterson: How do I prove by the principal of mathematical induction? 1.n+2.(n-1)+3.(n-2)+.....+(n-2).3+(n-1).2+n.1=(n(n+1)(n+2))/6 Answered by Paul Betts.
	1+4+9+16+...n^2 = n(n+1)(2n+1)/6		2000-06-01
		From Shamus O'Toole: How do you derive that for the series 1+4+9+16+25.. that S(n)=(n(n+1)(2n+1))/6 Answered by Penny Nom.
	Induction		2000-03-16
		From William Tsang: I am trying to prove a induction question Sigam r=1 n (2r -1)cube = n square (2 n square - 1) Answered by Harley Weston.
	Mathematical deduction and mathematical induction		2000-03-07
		From Espera Pax: What are mathematical deduction and mathematical induction, and what is the difference between them? Answered by Harley Weston.
	Logic and mathematical logic		1999-10-06
		From Polly Mackenzie: What is the difference between logic and math logic? Answered by Walter Whiteley.
	Mathematical Induction and the Derivative		1997-03-18
		From Shuling Chong: "Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n." Any educated tries are appreciated. Answered by Penny Nom.

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