Let Sk be sum of an infinite G.P. whose first term is k and common ratio is (1/k+1). Then displaystyle∑k=110 Sk is equal to

Question

Let Sk be sum of an infinite G.P. whose first term is k and common ratio is (1/k+1). Then displaystyle∑k=110 Sk is equal to  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Sk=(k/1-(1)k+1)=k+1 displaystyle∑k=110 Sk= displaystyle∑k=110(k+1)=(10 × 11/2)+10=65

Q. Let $S_{k}$ be sum of an infinite $G . P$ . whose first term is $k$ and common ratio is $\frac{1}{k + 1}$ . Then $k = 1 \sum 10 S_{k}$ is equal to ____