Search any question & find its solution
Question:
Answered & Verified by Expert
$\frac{1}{2 \cdot 3}+\frac{1}{4 \cdot 5}+\frac{1}{6 \cdot 7}+\frac{1}{8 \cdot 9}+\ldots$ is equal to
Options:
Solution:
1867 Upvotes
Verified Answer
The correct answer is:
$\log \left(\frac{e}{2}\right)$
$\begin{aligned} & \frac{1}{2 \cdot 3}+\frac{1}{4 \cdot 5}+\frac{1}{6 \cdot 7}+\frac{1}{8 \cdot 9}+\ldots \infty \\ & =\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)+\left(\frac{1}{8}-\frac{1}{9}\right)+\ldots \infty \\ & =1-\log _e 2 \\ & =\log _e e-\log _e 2 \\ & =\log \left(\frac{e}{2}\right)\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.