The sum of the series 1+11+2+11+2+3+ up to 10 terms, is:

Question

The sum of the series $1+\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\cdots$ up to 10 terms, is:

Accepted Answer

$T_r=\dfrac{1}{1+2+\cdots+r}=\dfrac{2}{r(r+1)}=2\left(\dfrac1r-\dfrac1{r+1}\right)$.

$$S_{10}=2\left(1-\frac{1}{11}\right)=2\times\frac{10}{11}=\frac{20}{11}.$$

Solutions · 1