Sequences and Series · Mathematics · TS EAMCET

If $1 \cdot 3 \cdot 5+3 \cdot 5 \cdot 7+5 \cdot 7 \cdot 9 \ldots$ to $n$ terms $=n(n+1) f(n)$, then $f(2)=$

Assertion (A) : $1+\frac{2 \cdot 1}{3 \cdot 2}+\frac{2 \cdot 5}{3 \cdot 6} \frac{1}{4}+\frac{2 \cdot 5 \cdot 8}{3 \cdot 6 \cdot 9} \frac{1}{8}+\ldots \infty=\sqrt[3]{4}$

Reason (R) : |x| < 1,(1-x) $=1+n x+\frac{n(n+1)}{1 \cdot 2} x^2$$+\frac{n(n+1)(n+2)}{1 \cdot 2 \cdot 3} x^{3}+\ldots$

The correct answer is :

Among the following four statements, the statement which is not true, for all $n \in N$ is

$\frac{1}{3 \cdot 6}+\frac{1}{6 \cdot 9}+\frac{1}{9 \cdot 12}+\ldots \ldots .$. to 9 terms $=$

When $|x|<2$, then coefficient of $x^2$ in the power series expansion of $\frac{x}{(x-2)(x-3)}$, is