Question

Use mathematical induction to prove 7^(n) − 1 is divisible by 6, for each integer n ≥ 1.

Answer #1

Prove by mathematical induction: n3 – 7n + 3 is divisible by
3, for each integer n ≥ 1.

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

Use mathematical induction to prove that for each integer n ≥ 4,
5n ≥ 2 2n+1 + 100.

Use Mathematical Induction to prove that 3n < n! if n is an
integer greater than 6.

Use the Strong Principle of Mathematical Induction to prove that
for each integer n ≥28, there are nonnegative integers x and y such
that n= 5x+ 8y

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

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 that 7^(n) − 1 is divisible by 6, for every positvie
integer n

Use Mathematical Induction to prove that for any odd integer n
>= 1, 4 divides 3n+1.

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

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