WBJEE · Maths · Binomial Theorem
The coefficient of \(x^n\), where \(n\) is any positive integer, in the expansion of \(\left(1+2 x+3 x^2+\ldots \ldots \ldots\right)^{1 / 2}\) is
- A 1
- B \(\frac{n+1}{2}\)
- C \(2 n+1\)
- D \(\mathrm{n}+1\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\[ s=1+2 x+3 x^2 . \] .\(\infty\) Hints : \(\frac{x S=x+2 x^2+\ldots \ldots \ldots \ldots}{s(1-x)=1+x+x^2+\ldots \ldots \ldots . \infty}\) \[ s=\frac{1}{(1-x)^2} \] \[ f(x)=\frac{1}{1-x}, f(x)=(1-x)^{-1}=1+x+x^2+x^3 \ldots \ldots \ldots \ldots . . .0=1 \]
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