Question

The sum of 1/1+root2+1/root2+root3+1/root3+root4 upto 99 terms​

Answer 1

Answer:

1/(sqrt1+ sqrt2) + 1/(sqrt2 + sqrt3) + ....+ 1/(sqrt99+ sqrt100)

We know that:

1/(sqrta + sqrt(1+a) = sqrt(a+1) -sqrta

==>sqrt2 - sqrt1 + sqrt3 -sqrt2 + ...+ sqrt100 -sqrt99

= -sqrt1 + sqrt100

= -1 + 10

= 9

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