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  4. The sum of the series: (2)2 + 2(4)2 + 3(6)2 +... upto 10 terms is :

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Q. The sum of the series :
$(2)^2 + 2(4)^2 + 3(6)^2 +...$ upto 10 terms is :

JEE MainJEE Main 2013Sequences and Series

Solution:

$2^{2}+2\left(4\right)^{2}+3\left(6\right)^{2}+...... upto\, 10\, terms$
$=2^{2}\left[1^{3}+2^{3}+3^{3}+......upto\, 10\, terms\right]$
$=4.\left(\frac{10\times11}{2}\right)^{2}=12100$