Question

prove by induction that n(n+1)(n+2) is divisible by 6 for n=1,2...

Answer #1

Consider the following expression: 7^n-6*n-1
Using induction, prove the expression is divisible by 36.
I understand the process of mathematical induction, however I do
not understand how the solution showed the result for P_n+1 is
divisible by 36? How can we be sure something is divisible by 36?
Please explain in great detail.

Prove by induction that if n is an odd natural number,
then 7n+1 is divisible by 8.

Prove that 5n2 +15n is divisible by 10 for every n ≥ 2, by
mathematical induction.

Prove by induction that 5^n + 12n – 1 is divisible by 16 for all
positive integers n.

Discrete math
Use mathematical induction to prove that n(n+5) is divisible by
2 for any positive integer n.

Prove using induction that for any m,n is an element
of natural number, if |{1,2,....,m}|= |{1,2,...,n}| then n=m

Prove by induction that 5n + 12n – 1 is divisible by 16 for all
positive integers n.

Prove by induction that k ^(2) − 1 is divisible by 8 for every
positive odd integer k.

Prove by induction.
a ) If a, n ∈ N and a∣n then a ≤ n.
b) For any n ∈ N and any set S = {p1, . . . , pn} of prime
numbers, there is a prime number which is not in S.
c) Prove using strong induction that every natural number n >
1 is divisible by a prime.

(10) Use mathematical induction to prove that
7n – 2n is divisible by 5
for all n >= 0.

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