JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

Let

x > 1

and for each positive integer

n

, define

\begin{aligned} s_n(x)= & \frac{x}{x+1}+\frac{x^2}{(x+1)\left(x^2+1\right)}+\frac{x^4}{(x+1)\left(x^2+1\right)\left(x^4+1\right)}+ \\ & \cdots+\frac{x^{2-1}}{(x+1)\left(x^2+1\right) \cdots\left(x^{2^{6-1}}+1\right)} \end{aligned}

Then

\lim \limits_{{n \rightarrow \infty}} s_n(x)

is equal to

View answer and explanation

Correct option: A

Option A is correct. By manipulating the series and taking the limit as n approaches infinity, the sum converges to 1.

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