Let `S=(sqrt(1))/(1+sqrt1+sqrt(2))+sqrt(2)/(1+sqrt(2)+sqrt(3))+(sqrt(3 – InterviewSolution

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1.	Let `S=(sqrt(1))/(1+sqrt1+sqrt(2))+sqrt(2)/(1+sqrt(2)+sqrt(3))+(sqrt(3))/(1+sqrt(3)+sqrt(4))+...+(sqrt(n))/(1+sqrt(n)+(sqrtn+1))=10` Then find the value of n.
Answer» Correct Answer - n=24 `T_(r)=(sqrtr)/(1+sqrtr+sqrt(r+1))=(sqrtr{1+sqrtr-sqrt(r+1)})/(1+r+2sqrtr-(r+1))` `=1/2{1+sqrtr-sqrt(r+1)}` `thereforeS_(n)=1/2(n+1)-sqrt(n+1)=10` Let `sqrt(n+1)`=x `thereforex^(2)-x=20` `rArrx^(2)-x-20=0` `rArrx=sqrt(n+1)=5` `thereforen=24`

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