(1)Prove 6^(2n)-4^(2n) must be a mutiple of 20 (2)Prove 6^(2n)+4^(2n)-2 must be a multiple of 50

(1)Prove 6^(2n)-4^(2n) must be a mutiple of 20

(2)Prove 6^(2n)+4^(2n)-2 must be a multiple of 50

Expert Solution

Colby Messinger answered 2 years ago

Use induction to prove that 2 + 4 + 6 + ... + 2n = n2...

Use induction to prove that 2 + 4 + 6 + ... + 2n = n2 + n for n ≥ 1. Prove this theorem as it is given, i.e., don’t first simplify it algebraically to some other formula that you may recognize before starting the induction proof. I'd appreciate if you could label the steps you take, Thank you!

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for...

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for all integers n Show all work

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2)...

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(5.1.24) Prove that 1/(2n) ≤ [1 · 3 · 5 · · · · · (2n...

(5.1.24) Prove that 1/(2n) ≤ [1 · 3 · 5 · · · · · (2n − 1)]/(2 · 4 · · · · · 2n) whenever n is a positive integer

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Prove by induction that: 1) x^n - 1 is divisible by x-1 2)2n < 3^n for...

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1. Use the ę notation to prove the following limits: lim n→∞ [n^2+ 3ncos(2n+1)+2] / [n^2−nsin(4n+3)+4]...

1. Use the ę notation to prove the following limits: lim n→∞ [n^2+ 3ncos(2n+1)+2] / [n^2−nsin(4n+3)+4] = 1 2. Let {an} a sequence converging to L > 0. Show ∃N ∈ N, ∀n ∈ N, n ≥ N, an > 0 3.Let {an} a sequence converging to L. Let {bn} a sequence such that ∃Nb ∈ N, ∀n ∈ N, n ≥ Nb, an = bn. Show that {bn} converges to L as well. Thank you. Please complete proofs fully.

int 50+20 * (50/4) /4

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