JEE Main 2013 (Online) 23rd AprilQuestion 1
The sum of the series : $(2)^{2}+2(4)^{2}+3(6)^{2}+\ldots$ upto $10$ terms is :
Sequence and Series · Standard Sums (Σ formulas)
Solution
Formulas used. (1) $\sum_{k=1}^{n}k^3=\left[\frac{n(n+1)}{2}\right]^2$Step 1 - General term. $k(2k)^2=4k^3$. Step 2 - Sum of $10$ terms. $$4\left(\frac{10\times11}{2}\right)^2=4\times3025=12100 .$$ Answer: (C)