The sum of the series $$22+2(4)2+3(6)2+$$… upto $$10$$ terms

given $$sum=2213+23+$$…$$+10$$ terms $$=410$$×$$1122=12100$$ formula $$nn+122$$

Series of natural numbers

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Question

$The sum of the series 2^{2} + 2 (4)^{2} + 3 (6)^{2} + \dots upto 10 terms$

Solution

$\begin{aligned} g i v e n s u m = 2^{2} (1^{3} + 2^{3} + \dots + 10 terms) \\ = 4 {(\frac{10 \times 11}{2})}^{2} = 12100 (f o r m u l a {[\frac{n (n + 1)}{2}]}^{2}) \end{aligned}$

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