Q84 / 160 · WBJEE 2009 · Mathematics
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
- Correct answerA1
- B$\frac{n+1}{2}$
- C$2 n+1$
- D$\mathrm{n}+1$
Solution
$$
s=1+2 x+3 x^2 .
$$
.$\infty$
Hints : $\frac{x S=x+2 x^2+\ldots \ldots \ldots \ldots}{s(1-x)=1+x+x^2+\ldots \ldots \ldots . \infty}$
$$
s=\frac{1}{(1-x)^2}
$$
$$
f(x)=\frac{1}{1-x}, f(x)=(1-x)^{-1}=1+x+x^2+x^3 \ldots \ldots \ldots \ldots . . .0=1
$$
Hence, the correct answer is option: 'A'.