Question

find general formula for the sequence
$1 + \frac{2}{1 + 2 } + \frac{3}{1 + 2 + 3} .....n \: terms$
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Answer 1

$\mathrm{The \: r^{th} \: term \: is}\\</p><p>T_{r}= \frac{r}{1+2+ \cdots +r}\\</p><p>T_r =\frac{r}{\frac{r (r+1) }{2}}\\</p><p>T_r =\frac{2}{r+1}$