Question

 

SOS

 

Answer 1

\(A=2\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+....+\dfrac{1}{99.100}\right)\)

\(=2\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+....+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

\(=2\left(\dfrac{1}{10}-\dfrac{1}{100}\right)=2.\dfrac{9}{100}=\dfrac{9}{50}\)

Answer 2

`A = 2/(10.11)+2/(11.12)+2/(12.13)+...+2/(99.100)`

`= 2(1/10 - 1/11  + 1/11 - 1/12 + ...-1/100)`

`= 2(1/10-1/100)`

`= 2 . 9/100`

`= 18/100 = 9/50`