S=90^2 +91^2 +.....+100^2 = ??


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Question Number 154456 by puissant last updated on 18/Sep/21

$S = 90^{2} + 91^{2} + . . . . . + 100^{2} = ? ?$
Commented by Rasheed.Sindhi last updated on 18/Sep/21

$S = (1^{2} + 2^{2} + . . . + 100^{2}) - (1^{2} + 2^{2} + . . . + 89^{2})$ $C o n t i n u e$
Commented by puissant last updated on 18/Sep/21

$T h a n k y o u$
	Answered by amin96 last updated on 18/Sep/21

	$S = 1^{2} + 2^{2} + 3^{2} \dots + 100^{2} - (1^{2} + 2^{2} + \dots + 89^{2})$ $\underset{n = 1}{\sum^{n}} k^{2} = \frac{n (n + 1) (2 n + 1)}{6}$ $S = \frac{100 \cdot 101 \cdot 201}{6} - \frac{89 \cdot 90 \cdot 179}{6} =$ $= 50 \cdot 67 \cdot 101 - 89 \cdot 15 \cdot 179 = 338350 - 238965 = 99385$
	Commented by puissant last updated on 18/Sep/21

	$T h a n k y o u$
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