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The value of sum(n=0)^(1947) 1/(2^(n)...

The value of
`sum_(n=0)^(1947) 1/(2^(n)+sqrt(2^(1947)))`
is equal to

A

`487/(sqrt(2^(1945)))`

B

`1946/(sqrt(2^(1947)))`

C

`1947/(sqrt(2^(1947)))`

D

`1948/(sqrt(2^(1947)))`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(n=0)overset(1947)sum1/(2^(n)+sqrt(2^(1947)))" Total terms "=1948`
`T_(1)=1/(1+sqrt(2^(1947)))`
`T_(1948)=1/(2^(1947)+sqrt(2^(1947)))`
`T_(1)+T_(1948)=1/(sqrt(2^(1947)))`
Similarly, `T_(2)+T_(1947)=1/(sqrt(2^(1947)))=T_(3)+T_(1946)=" and so an".........`
`" Total"1948/2=974" pairs"`
`:." Sum"=974/sqrt(2^(1947))=974/(sqrt(4xx2^(1945)))=487/(sqrt(2^(1945)))`
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