Question

Find the $(2n{)}^{th}$ term of the series whose $n^{th}$ term is $\frac{n^2+1}{n^3}$:

• A. $\frac{n^2+1}{8n^3}$
• B. $\frac{4n^2+1}{8n^3}$
• C. $\frac{4n^2+1}{n^3}$
• D. $\frac{2n^2+1}{2n^3}$

Answer 1

The correct option is B $\frac{4n^2+1}{8n^3}$

$T_{2n}=\frac{{\left(2n\right)}^2+1}{{\left(2n\right)}^3}=\frac{4n^2+1}{8n^3}$