Question

Calculate the $n^{th}$ term of the sequence $\frac{1}{2}+\frac{4}{4}+\frac{9}{8}+......$.

• A. $\frac{n^2}{2n}$
• B. $\frac{n^2}{2^n}$
• C. $\frac{n}{2^n}$
• D. None of these

Answer 1

The correct option is B $\frac{n^2}{2^n}$

Given series is $\frac{1}{2}+\frac{4}{4}+\frac{9}{8}+.......$

It is seen that the numerator is moving in sequence like $1^2,2^2,3^2.........$ and so on.

And the denominator is moving in sequence like $2^1,2^2,2^3.........$ and so on.

Thus the sequence is $\frac{1^2}{2^1},\frac{2^2}{2^2}........$and so on.

Thus the $n^{th}$ term is $\frac{n^2}{2^n}$.