Question

The middle term in the expansion of ( 1 - (1/X))^n(1-X)^n in the powers of X is:
A. -2nCn-1
B. -2nCn
C. 2nCn
D. 2nCn-1​

Answer 1

²ⁿCₙ The middle term in the expansion of (1  - (1/X))ⁿ(1 - X)ⁿ

Step-by-step explanation:

(1  - (1/X))ⁿ(1 - X)ⁿ

= ((X - 1)/X)ⁿ(1 - X)ⁿ

= ((1 - X)/(-X))ⁿ(1 - X)ⁿ

= (1 - X)ⁿ(1- X)ⁿ/(-X)ⁿ

= (1 - X)²ⁿ/(-X)ⁿ

Middle term would be  n + 1 th term

= ²ⁿCₙ (1)ⁿ(-X)ⁿ/(-X)ⁿ

=  ²ⁿCₙ

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Answer 2

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Refer the attachment.