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The sum to infinity of the series 1+2/...

The sum to infinity of the series `1+2/3+6/(3^2)+(10)/(3^3)+(14)/(3^4). . . . . .` is

A

3

B

4

C

6

D

2

Text Solution

Verified by Experts

The correct Answer is:
a
Let `S = 1+2/3 +6/(3^(2))+10/(3^(3))+14/(3^(4))+…`
`rArr S-1=2/3 +6/(3^(2))+10/(3^(3))+14/(3^(4))+…" "` …(i)
` rArr (S-1)/3 = 2/(3^(2))+6/(3^(3)) +10/(3^(4))+14/(3^(5))+…" "` ….(ii) ,
On subtracting Eq. (ii) from Eq.(i) ,we get
`2/3 (S-1)= 2/3 +4/(3^(2))+4/(3^(3)) +4/(3^(4))+...`
`rArr S-1 =1 +2/3 +2/(3^(3))+2/(3^(3))+...`
` rArr S= 2+(2/3)/(1-1/3)=2 +1=3`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-SEQUENCES AND SERIES -EXERCISE 21
  1. The sum to infinity of the series 1+2/3+6/(3^2)+(10)/(3^3)+(14)/(3^4...

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