SOLUTION: Using math of induction show that 2^n + (-1)^n+1 is divisible by 3

Question 1137651: Using math of induction show that 2^n + (-1)^n+1 is divisible by 3
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Base case: n=1

Hypothesis: Assume is divisible by 3 for n=k

Step case: Let n=k+1:

We know is divisible by 3 (by hypothesis)

Look at V-W:

=

The last two terms combine to -2 when k is odd, +2 when k is even, factor
out 2:
=

Noting that :
=

By the hypothesis, the factor is divisible by 3
We know W is divisible by 3 and V-W is also divisible by 3, so V = (W)+(V-W) is also divisible by 3.

DONE

RELATED QUESTIONS
Prove using math induction 2^n + (-1)^n+1 is divisible by... (answered by math_helper)

By the method of induction, show that 10^n+3.4^(n+1)+5 is divisible by... (answered by jim_thompson5910)

using mathematicsl induction prove that 3^n+7^n-2 is divisible by... (answered by Edwin McCravy)

Show by the Principle of Mathematical Induction: 5n � 1 is divisible by 2 for all n>=1 (answered by stanbon)

Use induction to show that 5^n-1 is divisible by... (answered by FrankM)

Prove by mathematical induction that: 2^2n - 1 is divisible by 3 for all positive... (answered by Edwin McCravy)

prove that the sum of all natural numbers divisible by 5 is equal to 5n(n+1)/2 using... (answered by Edwin McCravy)

proof this statement using math induction :... (answered by Edwin McCravy,ikleyn)

Use mathematical induction to prove each statement is true for all positive integers n:... (answered by math_helper)