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Let S=1/(1.4)+1/(4.7)+1/(7.10)+.....+ n ...

Let `S=1/(1.4)+1/(4.7)+1/(7.10)+.....+ n ` terms observe the following lists

A

`(1)/(6)`

B

`(1)/(2)`

C

`(1)/(4)`

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
The sum of infinite ………….
`S = (1)/(1.4)+(1)/(4.7)+………oo = sum_(r=1)^(oo) (1)/((3r-2)(3r+1))`
`= (1)/(3) sum_(r=1)^(oo) ((1)/(3r-2)-(1)/(3r+1))`
`= (1)/(3)(1-(1)/(4)+(1)/(4)-(1)/(7)+………)= (1)/(3)`
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