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The value of 2xx.^(n)C(1) + 2^(3) xx .^(...

The value of `2xx.^(n)C_(1) + 2^(3) xx .^(n)C_(3) + 2^(5) + "…."` is

A

`(3^(n)+(-1)^(n))/(2)`

B

`(3^(n)-(-1)^(n))/(2)`

C

`(3^(n) + 1)/(2)`

D

`(3^(n) - 1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(1+2)^(n) - (1-2)^(n) = 2[.^(n)C_(1)xx2+.^(n)C_(3)xx2^(3)+.^(n)C_(5)xx2^(5)+"….."]`
`:. .^(n)C_(1)xx2+.^(n)C_(3)xx2^(3)+.^(n)C_(5)xx2^(5)+"…."= (3^(n)-(-1)^(n))/(2)`
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