सरल करें:
`1/(sqrt(100)-sqrt(99))-1/(sqrt(99)-sqrt(98))`
`+1/(sqrt(98)-sqrt(97))-1/(sqrt(97)-sqrt(96))`
`+………..+1/(sqrt(2)-sqrt(1))`

Options

A. 10
B. 9
C. 13
D. 11

Answer

D

Explanation

`1/(sqrt(100)-sqrt(99))xx(sqrt(100)+sqrt(99))/(sqrt(100)+sqrt(99))`
`implies (sqrt(100)+sqrt(99))/1impliessqrt(100)+sqrt(99)`
Similarly
`implies1/(sqrt(99)-sqrt(98))impliessqrt(99)+sqrt(98)`
`implies 1/(sqrt(98)-sqrt(97))impliessqrt(98)+sqrt(97)`……… and so on
Now expression
`implies sqrt(100)+sqrt(99)-sqrt(99)-sqrt(98)+sqrt(98)+sqrt(97)............+sqrt(2)+1`
`implies sqrt(100)+1implies10+1=11`