5^{2}+6^{2}+7^{2}+ldots+20^{2} = | vedclass

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(B) We need to find the sum $S = 5^{2} + 6^{2} + 7^{2} + \ldots + 20^{2}$.This can be expressed as the difference of two sums of squares:$S = \sum_{k=

Vedclass · Accepted Answer

$2840$

Vedclass · Answer

(B) We need to find the sum $S = 5^{2} + 6^{2} + 7^{2} + \ldots + 20^{2}$.This can be expressed as the difference of two sums of squares:$S = \sum_{k=1}^{20} k^{2} - \sum_{k=1}^{4} k^{2}$.Using the formula $\sum_{k=1}^{n} k^{2} = \frac{n(n+1)(2n+1)}{6}$:For $n=20$: $\sum_{k=1}^{20} k^{2} = \frac{20(21)(41)}{6} = 10 	imes 7 	imes 41 = 2870$.For $n=4$: $\sum_{k=1}^{4} k^{2} = \frac{4(5)(9)}{6} = 2 	imes 5 	imes 3 = 30$.Therefore,$S = 2870 - 30 = 2840$.

$5^{2}+6^{2}+7^{2}+\ldots+20^{2} =$

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