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Question Number 36365 by chakraborty ankit last updated on 01/Jun/18

Commented by tanmay.chaudhury50@gmail.com last updated on 01/Jun/18

$r e p o s t q u e s t i o n n o 11 a n d 12$
Commented by chakraborty ankit last updated on 02/Jun/18

$o k s i r$
	Answered by tanmay.chaudhury50@gmail.com last updated on 01/Jun/18
	$s_n =2+3+6+11+18+...+T_(n−1) +T_n s_n = 2+3+6+11+...+T_(n−2) +T_(n−1) +T_n shifting one place rivhtward then subsgructing 0=2+(1+3+5+7+...−T_n ) T_n =2+((n−1)/2){2×1+(n−1−1)×2} T_n =2+((n−1)/2){2n−2} T_n =2+(n−1)(n−1) T_n =n^2 −2n+3 T_(50) =50^2 −2×50+3 =2500−100+3 =2403 49^2 +2 is ans$
	$s_{n} = 2 + 3 + 6 + 11 + 18 + . . . + T_{n - 1} + T_{n}$ $s_{n} = 2 + 3 + 6 + 11 + . . . + T_{n - 2} + T_{n - 1} + T_{n}$ $s h i f t i n g o n e p l a c e r i v h t w a r d t h e n s u b s g r u c t i n g$ $0 = 2 + (1 + 3 + 5 + 7 + . . . - T_{n})$ $T_{n} = 2 + \frac{n - 1}{2} {2 \times 1 + (n - 1 - 1) \times 2}$ $T_{n} = 2 + \frac{n - 1}{2} {2 n - 2}$ $T_{n} = 2 + (n - 1) (n - 1)$ $T_{n} = n^{2} - 2 n + 3$ $T_{50} = 50^{2} - 2 \times 50 + 3$ $= 2500 - 100 + 3$ $= 2403$ $49^{2} + 2 i s a n s$
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