We mathematical induction to prove the statement is true for all positive integers n. 8+16+24 + ... + 8n=4n (n+1)

Assume its true for n = k

then 8 + 16 + 24 + ... + 8k = 4k (k + 1)

sum for k+1 terms = 4k (k + 1) + 8 (k + 1)

= 4 (k + 1) ((k + 2)

= 4 (k + 1) (k + 1 + 1)

Now this is the same as the formula for k terms with the k being replaced by k + 1. So if the formula is correct for k terms then its must also be correct for k+1 terms

Also its true for k = 1 because 8 = 4 (1) (1 + 1) so its true for k = 2,3 4 and so

on. - for all values of k (n).

This compleres the proof.