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  4. Let S =(3/2)+(3/6)+(3/12)+(3/20)+ ldots ∞ then S is equal to

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Q. Let $S =\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+\frac{3}{20}+\ldots \infty$ then $S$ is equal to

Sequences and Series

Solution:

$S =3\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\ldots\right)$
$S =3\left(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\ldots .\right)$
$\therefore S =3$