Question

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.

4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = (4(4n+1)(8n+7))/6

Answer 1

@satellite73

Answer 2

Step 1. Let P(n) : 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = (4(4n+1)(8n+7))/6

Step 2. Prove that P(1) is true.

Step 3: Assume it is true for P(k) where k is a natural number.

Step 4: We now prove that P(K+1) is true for every P(K)

These are the basic steps.

Answer 3

What's P(1)?

Answer 4

We will prove that the expression is true when we put n=1.

Answer 5

So we plug in n=1 on the right of the = sign?

Answer 6

when we plug n=1 in left and right side of =, then both should be equal..
just make a try

Answer 7

I don't understand how to plug it in on the left side...