An algebra problem by shivamani patil

We have formula as $\frac { 1 }{ n(n+1) }$

We can split it as $\frac { 1 }{ n } -\frac { 1 }{ n+1 }$

therefore we have

$\left( \frac { 1 }{ 1 } -\frac { 1 }{ 2 } \right) +\left( \frac { 1 }{ 2 } -\frac { 1 }{ 3 } \right) +\left( \frac { 1 }{ 3 } -\frac { 1 }{ 4 } \right) +..............+\left( \frac { 1 }{ 99 } -\frac { 1 }{ 100 } \right)$

Now we cancel terms and we get $1-\frac { 1 }{ 100 }$

i.e 0.99

it is not mathematical sol. but it is useful to find out ans of these type of ques. First term is 1/2 and second term is 1/6 Now add both of them it comes out to be n/n+1 , here n=2 , so it is 2/3 .In the ques there are 99 terms. So ans is 99/100