Use mathematical induction to prove the following statement: The sum of the first n even positive integers is (n2 + n). That is, 2 4 6 8 2n

Step-by-step explanation:

To prove that the sum of the first n even +ve integers is:

By using mathematical induction;

For n = 1, we get:

2n = 2 × 1 = 2

2 = 1² + 1 ----- (1)

∴ the outcome is true if n = 1

However, let assume that the result is also true for n = k

Now,

we can now say:

∴

Thus, the result is true for n = m+1, hence we can posit that the result is also true for each value of n.

As such

45

step-by-step explanation: