`1/(sqrt(2)+1+1/(sqrt(3)+sqrt(2))+1/(sqrt(4)+sqrt(3))+…..+ 1/(sqrt(100)+sqrt(99))` का मान ज्ञात करें।

Options

A. `1`
B. `9`
C. `sqrt(199)`
D. `sqrt(99)-1`

Answer

B

Explanation

`1/(sqrt(2)+1)=1/(sqrt(2)+1)xx(sqrt(2)-1)/(sqrt(2)-1)`
`implies((sqrt(2)-1)/(2-1))=sqrt(2)-1`
Similarly
`implies1/(sqrt(3)+sqrt(2)=sqrt(3)-sqrt(2)` and so on.
Now put value
`impliessqrt(2)-1+sqrt(3)-sqrt(2)+sqrt(4)-sqrt(3)…………`
`+ sqrt(100)-sqrt(99)`
`implies sqrt(100)-1implies10-1=9`