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What is the sum of the series 1-(1)/(2)+...

What is the sum of the series `1-(1)/(2)+(1)/(4)-(1)/(8)+....` equal to?

A

`(1)/(2)`

B

`(3)/(4)`

C

`(3)/(2)`

D

`(2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`1-(1)/(2)+(1)/(4)-(1)/(8)+…" can be written as"`
`1+(-(1)/(2))+(-(1)/(2))^(2)+(-(1)/(2))^(3)+…`
`[because" This is a GP with first term =1 and common ratio "=-(1)/(2)]`
So, sum of the series
`=(1)/(1-(-(1)/(2)))=(1)/(1+(1)/(2))=(2)/(3)`
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