Let p=1+1/(sqrt(2))+1/(sqrt(3))+...+1/(s...

Let `p=1+1/(sqrt(2))+1/(sqrt(3))+...+1/(sqrt(120))` and `q=1/(sqrt(2))+1/(sqrt(3))+...+1/(sqrt(121))` then

`pgt20`

`qlt20`

`p+qlt40`

`p+qgt40`

Text Solution

Verified by Experts

The correct Answer is:

A, B, D

Consider function `f(x)=1/(sqrt(x))` for `1lt x lt 121`

Clearly `p gt int_(1)^(121)1/(sqrt(x))dx=20`

and `q lt int_(1)^(121)1/(sqrt(x))dx=20`
`:.p-20gt20-q`
`implies p+qgt40`

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