1 1.2 + 1 2.3 + 1 3.4 +.......+ ......... 1 n . ( n + 1 ) equals Options: A . &nbsp 1 n ( n + 1 ) B . &nbsp n n + 1 C . &nbsp 2 n n + 1 D . &nbsp 2 n ( n + 1 )

Answer: Option B : B ( 1 1 - 1 2 ) + ( 1 2 - 1 3 ) + ( 1 3 - 1 4 ) + .........+ ( 1 n - 1 n + 1 ) = 1 - 1 n + 1 = n n + 1

11.2 + 12.3 + 13.4 +.......+ ......... 1n.(n+1) equals

Question

$\frac{1}{1.2}$ +
$\frac{1}{2.3}$ +
$\frac{1}{3.4}$ +.......+ .........
$\frac{1}{n . (n + 1)}$ equals

Options:

A .

\frac{1}{n (n + 1)}

B .

\frac{n}{n + 1}

C .

\frac{2 n}{n + 1}

D .

\frac{2}{n (n + 1)}

Answer: Option B
:
B

(
$\frac{1}{1}$ -
$\frac{1}{2}$ ) + (
$\frac{1}{2}$ -
$\frac{1}{3}$ ) + (
$\frac{1}{3}$ -
$\frac{1}{4}$ ) + .........+ (
$\frac{1}{n}$ -
$\frac{1}{n + 1}$ )

= 1 -
$\frac{1}{n + 1}$ =
$\frac{n}{n + 1}$

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