series 3

Calculus Level 2

Test the series: $\displaystyle\frac{2}{2\times3}+\displaystyle\frac{2}{3\times4}+\displaystyle\frac{2}{4\times5}+\displaystyle\frac{2}{5\times6}+\displaystyle\cdot\cdot\cdot$

it diverges neither of the answers it converges incocnclusive

1 solution

Anuj Mishra
Jun 22, 2015

Rth term, $T_{r} = \frac{2}{r*(r+1)}$ where $r \geq 2$

We can rearrange it and get, $T_{r}$ = $\frac{2}{r}$ - $\frac{2}{(r+1)}$

$\Rightarrow$ Sum of series, $S = 2*( \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} \ldots... )$

$\Rightarrow$ $S = 1$

As series has a finite value, hence it converges.

series 3

1 solution

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