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44 Answered Questions for the topic Mathematical Induction

Mathematical Induction Proofs

10/10/16

Proof by induction

1 × 3 + 3 × 5 + 5 × 7 + . . . + (2n − 1)(2n + 1) = n(4n2 + 6n − 1)/3.

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Mathematical Induction Proofs

10/10/16

proof by induction

Use the method of proof by induction to show that (1+x+x2 +. . .+xn-1)(1−x) = (1−xn), for all positive integers n

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Mathematical Induction Discrete Math Sequence Proof

05/03/16

Please help me with the proof below!

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n.Prove that ∀ n ∈ N, xn+6=xn by induction Please help me. I'm reviewing for my final and something like this may appear on it.

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Mathematical Induction Discrete Math Sequences Proof

05/03/16

Please help with proof by induction below

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n. Prove that ∀ n ∈ N, xn+6=xn by induction

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Mathematical Induction Math Discrete Math Proof

04/14/16

Please help me prove by induction the theorm below

let〈an〉∞n=1 and 〈bn〉∞ n=1 by sequences of numbers Then ∀ m∈N ∑(an+bn) = (∑an) +(∑bn) Proof by induction Side note: The summations go from n=1 to m

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Mathematical Induction Fibonacci Sequence Mathematical Proof Maths C

04/12/16

Prove formula for sum of Fibonacci sequence numbers by mathematical induction.

We need to prove the following using proof by induction. I don't want the actual answer if you can avoid it, I just can't figure out how to do it because when I do it how my notes read I am... more

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Mathematical Induction

03/21/16

prove by induction

Prove by Prove, using induction that 2^(n) ≤ 2^(n+1) − 2^(n−1) − 1 for all n ≥ 1

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Mathematical Induction Proofs Abstract Mathematical Proof

02/05/16

Prove Statement using the First Principle of Mathematical Induction

Prove the following statements using the First Principle of Mathematical Induction:(a) If r ≠ 1, then1 + r + r2 + ... + rn = (1 − rn+1)/(1-r) for all n ∈ N. Why does the formula not work when r =... more

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Mathematical Induction Inequalities Series

11/22/15

Trying to solve this proof by induction Series question

Prove Sn-1 > 2(n1/2 - 1) for all n ∈ Ν \ {1} where Sn = 1/√1 + 1/√2 + 1/√3 + ... + 1/√n I have set N = 2 for the basis step: S2-1 = 1/√1 > 2(√2 - 1) Which is true For the assumption... more

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