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If sum(r=0)^(2n) ar(x-100)^r= sum(r=0)^(...

If `sum_(r=0)^(2n) a_r(x-100)^r= sum_(r=0)^(2n) br(x-101)^r` and `a_k=(2^k)/(.^kC_n) AA k ge n ` then b_n equals (A) `2^n(2^(n+1)-1)` (B) `2^n(2^(n)-1)` (C) `2^n(2^(n)+1)` (D) `2^(n+1)(2^(n)-1)`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
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