Using mathematical induction prove whether or not the following statement is true for all positive integers n, or show why it is false.

2+6+10+ +4n-2=2n^2

Base case: For , the left side is 2 and the right is , so the base case holds.

Induction hypothesis: Assume the statement is true for , that is

We want to show that this implies truth for , that

The first terms on the left reduce according to the assumption above, and we can simplify the -th term a bit:

so the statement is true for all .

14

step-by-step explanation:

168

step-by-step explanation:

i am pretty sure that the answer is 168