Question

Find a formula in n, a, m, and d for the sum (a md) (a (m 1)d) (a (m 2)d) · · · (a (m n)d), where m and n are integers, n ≥ 0, and a and d are real numbers. justify your answer.

Answer 1

Write this as the sum of:
a+md
a+md+d
a+md+d+d
...
a+md+d+d+...+d

Total=n(a+md)+d(1+2+3+...+n-1)=n(a+md)+dn(n-1)/2