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

$$\mathrm{Given}1+3+5+7=16\mathrm{we}\mathrm{know}\mathrm{that}$$$$16=4^2\mathrm{and}4\mathrm{is}\mathrm{the}\mathrm{half}\mathrm{of}8\mathrm{which}\mathrm{is}\mathrm{the}$$$$\mathrm{successor}\mathrm{of}7.$$$$$$$$\mathrm{conjecture}\mathrm{the}\mathrm{result}\mathrm{of}\mathrm{this}\mathrm{sum}:$$$$1+3+5+7+...+25$$

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

$$13terms,and{13}^2=169$$$$$$$$Generally{T}_n=(2n-1)$$$$\underset{n=1}{\sum ^n}(2n-1)=n(n+1)-n=n^2$$

Commented by mathocean1 last updated on 05/Oct/20

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$$$$$

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

$$Successorof25is26.$$$$Halfof26is13.$$$$\therefore Thegivensum={13}^2=169$$

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