The sum to infinityof the series `1+2/3+6/(3^2)+(10)/(3^3)+(14)/(3^4). – InterviewSolution

InterviewSolution

1.	The sum to infinityof the series `1+2/3+6/(3^2)+(10)/(3^3)+(14)/(3^4). . . . . .`is(1) 2 (2) 3(3) 4 (4) 6A. 2B. 3C. 4D. 6
Answer» Correct Answer - B Let `S=1+2/3+6/3^(2)+10/3^(3)+14/3^(4)`+…. `therefore1/3S=1/3+2/3^(2)+6/3^(3)+10/3^(4)+….` subtracting (2) from (1), we get `S(1-1/3)=1+1/3+4/3^(2)+4/3^(3)+4/3^(4)+…..` `rArr2/3S=4/3+4/3^(2)(1+1/3+1/3^(2)+…)` `=4/3+4/3^(2)(1/(1-1/3)=4/3+4/3^(2)3/2=4/3+2/3=6/3` `rArrS=3`

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