Evaluate ∑_{k=1}^{n} k r^{k−1} (|r| ≠ 1).

Evaluate ∑_{k=1}^{n} k r^{k−1} (|r| ≠ 1).

A (1 − r^n)/(1 − r)

B (nr^{n} − (n − 1)r^{n+1})/(1 − r)^2

C (1 − (n + 1)r^n + n r^{n+1})/(1 − r)^2

D (1 − r^{n+1})/(1 − r)^2

Solution

Correct Answer: Option C