Given-1-3-5-7-16-we-know-that-16-4-2-and-4-is-the-half-of-8-which-is-the-successor-of-7-conjecture-the-result-of-this-sum-1-3-5-7-25-

Question Number 116683 by mathocean1 last updated on 05/Oct/20

Given 1 + 3 + 5 + 7 = 16 we know that

16 = 4^{2} and 4 is the half of 8 which is the

successor of 7 .

conjecture the result of this sum :

1 + 3 + 5 + 7 + \dots + 25

Answered by Dwaipayan Shikari last updated on 05/Oct/20

13 t e r m s, a n d 13^{2} = 169

G e n e r a l l y T_{n} = (2 n - 1)

\underset{n = 1}{\sum^{n}} (2 n - 1) = n (n + 1) - n = n^{2}

Commented by mathocean1 last updated on 05/Oct/20

thank you sir

Answered by $@y@m last updated on 06/Oct/20

S u c c e s s o r o f 25 i s 26 .

H a l f o f 26 i s 13 .

∴ T h e g i v e n s u m = 13^{2} = 169

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