Simplify the expression?: 1/(sqrt(144)+sqrt(145))+1/(sqrt(145)+sqrt(146))+...+1/(sqrt(168)+sqrt(169))

Simplify the expression:

1/(sqrt(144)+sqrt(145))+1/(sqrt(145)+sqrt(146))+...+1/(sqrt(168)+sqrt(169))

1 Answer
George C.
Mar 23, 2017

1

Explanation:

First note that:

1/(sqrt(n+1)+sqrt(n)) = (sqrt(n+1)-sqrt(n))/((sqrt(n+1)+sqrt(n))(sqrt(n+1)-sqrt(n))

color(white)(1/(sqrt(n+1)+sqrt(n))) = (sqrt(n+1)-sqrt(n))/((n+1)-n)

color(white)(1/(sqrt(n+1)+sqrt(n))) = sqrt(n+1)-sqrt(n)

So:

1/(sqrt(144)+sqrt(145))+1/(sqrt(145)+sqrt(146))+...+1/(sqrt(168)+sqrt(169))

=(sqrt(145)-sqrt(144))+(sqrt(146)-sqrt(145))+...+(sqrt(169)-sqrt(168))

=sqrt(169)-sqrt(144)

=13-12

=1

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