Question

Sum of the series S = 1 + $\frac{1}{2}$(1 + 2) + $\frac{1}{3}$(1 + 2 + 3) + $\frac{1}{4}$ (1 + 2 + 3 + 4) + .........upto 20 terms is

• A. 110
• B. 111
• C. 115
• D. 116

Answer 1

The correct option is C

115

We have

$\frac{1}{k}$(1 + 2 + 3 + .......+ k) = $\frac{1}{k}$ $\frac{k(k+1)}{2}$ = $\frac{k+1}{2}$

Thus, S = $\frac{1}{2}$[2 + 3 + 4 + .......21] = $\frac{10}{2}$(2 + 21) = 115