Search any question & find its solution
Question:
Answered & Verified by Expert
If $\quad 2^3+4^3+6^3+\ldots+2(n)^3=h n^2(n+1)^2$, then $h$ is equal to
Options:
Solution:
2029 Upvotes
Verified Answer
The correct answer is:
$2$
$\begin{aligned} \text { Let } S_n=2^3+4^3 & +6^3+\ldots+(2 n)^3 \\ & =\Sigma(2 n)^3=8 \Sigma n^3=8 \quad\left[\frac{n(n+1)}{2}\right]^2 \\ \Rightarrow 2 n^2(n+1)^2 & =h n^2(n+1)^2 \\ \Rightarrow \quad h & =2\end{aligned}$
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.