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If sum(k=4)^(143) (1)/(sqrt(k)+sqrt(k+1)...

If `sum_(k=4)^(143) (1)/(sqrt(k)+sqrt(k+1))=a-sqrt(b)` then a and b respectively are

A

`10` and `0`

B

`-10 and 4`

C

10 and 4

D

`-10 and 0`

Text Solution

Verified by Experts

The correct Answer is:
A
(i) Substitute the values of k and rationalize every term of LHS.
(ii) `underset(k=4)overset(143)sum(1)/(sqrt(k)+sqrt(k+1))=(1)/(sqrt(5)+sqrt(4))+(1)/(sqrt(6)+sqrt(5))+...+(1)/(sqrt(144)+sqrt(143))`
(iii) Rationalize the denominator two times.
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