Thank you for reporting, we will resolve it shortly
Q.
The sum to infinity of the series $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\ldots \ldots$ is equal to
Sequences and Series
Solution:
$S =\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\ldots \ldots$
$T _{ n }=\frac{1}{1+2+3+4+\ldots \ldots \ldots+ n }=\frac{2}{ n ( n +1)}=2\left[\frac{1}{ n }-\frac{1}{ n +1}\right\rceil \Rightarrow S _{\infty}=2$