Topic: mathematical induction list of topics
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23 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.
	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.
	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.
	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.
	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.
	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.
	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.
	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.
	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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