Question

The series $\frac{x}{1.2}+\frac{x^2}{2.3}+\frac{x^3}{3.4}+...(x>0)$ is not convergent where $x$ is ?

• A. $\frac{1}{2}$
• B. $1$
• C. $2$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $2$

$u_n=\frac{x^n}{n(n+1)}$
Now, ${lim}_{n\to \infty }\frac{u_n}{u_{n+1}}={lim}_{n\to \infty }\frac{n+2}{xn}=\frac{1}{x}>1$
Therefore, $x=2$ is the correct option.