We found 55 items matching your search.
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Mathematical induction |
2007-11-27 |
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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. |
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A faulty induction argument |
2007-10-31 |
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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. |
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Subsets of a set |
2007-10-30 |
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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. |
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Induction problem (divisible by 11) |
2007-08-29 |
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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. |
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Mathematical induction |
2007-03-02 |
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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. |
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cos(n)pi = (-1)^n |
2006-12-14 |
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From Idrees:
How can I prove the following: cos(n)pi = (-1)^n
Answered by Steve La Rocque. |
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The proof of inequality by mathematical induction |
2006-12-07 |
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From Carol:
S(n) = 2^n > 10n+7 and n>=10
Answered by Stephen La Rocque. |
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The Fibonacci sequence |
2006-11-21 |
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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. |
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Composition of functions |
2006-11-19 |
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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. |
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Induction |
2006-11-16 |
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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. |
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A proof by induction |
2006-11-06 |
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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. |
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Induction |
2006-10-31 |
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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. |
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A proof by induction |
2006-10-02 |
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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. |
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Proof by induction |
2006-04-24 |
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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. |
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Proving a summation formula by induction |
2006-04-19 |
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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. |
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