Question

Answer 1

`N=4/[2xx3]+4/[3xx4]+4/[4xx5]+...+4/[9900]`

`N=4/[2xx3]+4/[3xx4]+4/[4xx5]+...+4/[99xx100]`

`N=4xx(1/[2xx3]+1/[3xx4]+1/[4xx5]+...+1/[99xx100])`

`N=4xx(1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100)`

`N=4xx(1/2-1/100)`

`N=4xx49/100`

`N=49/25`

Answer 2

\(N=\dfrac{4}{2.3}+\dfrac{4}{3.4}+\dfrac{4}{4.5}+.....+\dfrac{4}{9900}\)

\(N=\dfrac{4}{2.3}+\dfrac{4}{3.4}+\dfrac{4}{4.5}+.....+\dfrac{4}{99.100}\)

`N=4 xx(2/(2xx3) + 2/(3xx4) + 2/(4xx5) + ...... + 1/(99xx100))`

`N=4 xx(1/(2xx3) + 1/(3xx4) + 1/(4xx5) + ...... + 1/(99xx100))`

`N=4 xx (1/2 - 1/3 + 1/3 - 1/4 + ..... 1/99 - 1/100)`

`N=4 xx ( 1/2 - 1/100)`

`N=4 xx ( 50/100 - 1/100)`

`N=4 xx 49/100`

`N=49/25`