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Question Number 94708 by abony1303 last updated on 20/May/20

Commented by abony1303 last updated on 20/May/20

$I^{'} m s o t i r e d s e e i n g t h e s e t y p e o f p r o b l e m s$ $i n m y e x a m . C a n s m n e x p l a i n t h e s e k i n d$ $o f q u e s t i o n s i n e a s y w a y ? O r s u g g e s t m e$ $t h e b o o k t o g e t i n f o r m a t i o n . p l s .$
	Answered by Worm_Tail last updated on 14/Jul/20

	$S_{n} = 2 + 2 + 4 + 4 + 4 + 4 + 6 + 6 + 6 + 6 + 6 + 6 + . . . + n + n + n$ $S_{n} = 2 (2) + 4 (4) + 6 (6) + . . . + 2 n (2 n)$ $S_{n} = \underset{r = 1}{\sum^{n}} 2 r (2 r) \Rightarrow$ $S_{n} = \underset{r = 1}{\sum^{n}} 4 r^{2}$ $S_{n} = 4 Σ r^{2} \Rightarrow S_{n} = 4 \frac{n (n + 1) (2 n + 1)}{6}$ $= \frac{2 (2019) (2020) (4039)}{3} = \frac{2 (2019) (4039)}{3} (2020)$ $\frac{S_{2019}}{10} = \frac{2 (2019) (4039)}{3} (202) r e m a i n d e r 0$
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