Question

Plzz rply in whole steps and in return,i will mark as brainliest if the ans is in whole steps​

Answer 1

Each of the given terms is of the form:

$\frac{1}{n * (n + 1)} = \frac{(n + 1) - n}{n * (n + 1)} = \frac{1}{n} - \frac{1}{n + 1}$

Applying the above, we get:

$(\frac{1}{1} - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + ... + (\frac{1}{100} - \frac{1}{101})$

Observe the 2nd term of the 1st bracket and the 1st term of the 2nd bracket - they cancel out.

Similarly, all the terms between $1$ and $-\frac{1}{101}$ cancel out, and leave:

$1 - \frac{1}{101} = \frac{100}{101}$