Question

$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+.....+\frac{1}{380}=.........$

• A. $\frac{1}{20}$
• B. $1$
• C. $\frac{19}{20}$
• D. $\frac{20}{19}$

Answer 1

Answer: (C)

$\frac{19}{20}$

It can be written as $\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\frac{1}{5\times 6}+..............+\frac{1}{19\times 20}$

It can be further expressed as

$\frac{1}{1}-\frac{1}{2}+\frac{1}{2}–\frac{1}{3}+\frac{1}{3}–\frac{1}{4}+.............-\frac{1}{18}+\frac{1}{18}–\frac{1}{19}+\frac{1}{19}–\frac{1}{20}$

Here all the terms get cancelled except the first and last one

$=1–\frac{1}{20}$

$=\frac{19}{20}$