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Prove that the coefficient of x^n in the...

Prove that the coefficient of `x^n` in the expansion of `(1+x)^(2n)` is twice the coefficient of `x^n` in the expansion of `(1+x)^(2n-1)`

A

`1 : 2`

B

`1 : 3`

C

`3 : 1`

D

`2 : 1`

Text Solution

AI Generated Solution

To prove that the coefficient of \( x^n \) in the expansion of \( (1+x)^{2n} \) is twice the coefficient of \( x^n \) in the expansion of \( (1+x)^{2n-1} \), we will follow these steps: ### Step 1: Identify the Coefficient of \( x^n \) in \( (1+x)^{2n} \) The general term in the binomial expansion of \( (1+x)^{2n} \) is given by: \[ T_{r+1} = \binom{2n}{r} x^r ...
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