Find the sum of the infinte series `(1)/(9)+(1)/(18)+(1)/(30)+(1)/(45) – InterviewSolution

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1.	Find the sum of the infinte series `(1)/(9)+(1)/(18)+(1)/(30)+(1)/(45)+(1)/(63)+…`A. `(1)/(3)`B. `(1)/(4)`C. `(1)/(5)`D. `(2)/(3)`
Answer» Correct Answer - A `(a)` `T_(n)=(1)/(3)[(1)/(3)+(1)/(6)+(1)/(10)+(1)/(15)+(1)/(21)+…]` `=(2)/(3)[(1)/(23)+(1)/(34)+(1)/(45)+(1)/(56)+…]` Hence `T_(n)=(2)/(3)(1)/((n+1)(n+2))` `=(2)/(3)[(1)/(n+1)-(1)/(n+2)]` `:.S_(oo)=(2)/(3)*(1)/(2)=(1)/(3)`

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