Question

The sum to infinity of the series $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots \dots$ is equal to

• A. 2
• B. 5/2
• C. 3
• D. none of these

Answer 1

Answer: (A)

$S=\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots \dots$
$T_n=\frac{1}{1+2+3+4+\dots \dots \dots +n}=\frac{2}{n(n+1)}=2[\frac{1}{n}-\frac{1}{n+1}\rceil \Rightarrow S_{\infty }=2$