Question

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

• A. 1
• B. 2
• C. 3/2
• D. 3

Answer 1

Answer: (D)

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