Use mathematical induction to prove that the statement is true for every positive integer n. 8 + 16 + 24 + . . + 8n = 4n(n + 1)

Induction on n

Base case: n = 0

the left side is 0, and the right side is 0, so the equality holds.

Now, suppose that is true for n, and you need to show that the equality holds for n+1

So, write the left side

8 + 16 +24 + ... + 8n + 8(n+1) (*)

By hypothesis, 8+16+24+ ...+ 8n = 4n(n+1)

so, in (*) we have

4n(n+1) +8(n+1) = (4n+8)(n+1) = 4(n+2)(n+1) = 4(n+1)(n+2). So, this is true for every natural number n.

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

answer: what are the following choices