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[" If "(1)/(2sqrt(1)+1sqrt(2))+(1)/(3sqr...

[" If "(1)/(2sqrt(1)+1sqrt(2))+(1)/(3sqrt(2)+2sqrt(3))+(1)/(4sqrt(3)+3sqrt(4))+...+(1)/(100sqrt(99)+99sqrt(100))=(a)/(b)],[" where "a" and "b" are positive co-prime integers then "(a^(2)+9)/(b)" is: "]

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(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))

(1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+...(1)/(sqrt(99)+sqrt(100))

Prove that (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+....+(1)/(sqrt(8)+sqrt(9))=2

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Simplify P=(1)/(2sqrt(1)+sqrt(2))+(1)/(3sqrt(2)+2sqrt(3))+...+(1)/(100sqrt(99)+99sqrt(100))

1/(1-sqrt(2))+ 1/(sqrt(2)-sqrt(3))+1/(sqrt(3)-sqrt(4))+..........+1/(sqrt(8)-sqrt(9))

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The value of (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+1/(sqrt(3)+sqrt(4))+........+(1)/(sqrt(8) + sqrt(9)) is