11^2 + 12^2 + 13^2 + dots + 20^2 = ? | vedclass

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(C) We need to calculate the sum $S = 11^2 + 12^2 + 13^2 + \dots + 20^2$.This can be expressed as the difference of two sums of squares:$S = \sum_{n=1

Vedclass · Accepted Answer

$2485$

Vedclass · Answer

(C) We need to calculate the sum $S = 11^2 + 12^2 + 13^2 + \dots + 20^2$.This can be expressed as the difference of two sums of squares:$S = \sum_{n=1}^{20} n^2 - \sum_{n=1}^{10} n^2$.Using the formula $\sum_{n=1}^{k} n^2 = \frac{k(k+1)(2k+1)}{6}$:For $k=20$: $\frac{20(21)(41)}{6} = 10 	imes 7 	imes 41 = 2870$.For $k=10$: $\frac{10(11)(21)}{6} = 5 	imes 11 	imes 7 = 385$.Therefore,$S = 2870 - 385 = 2485$.

$11^2 + 12^2 + 13^2 + \dots + 20^2 = ?$

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