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The-result-of-adding-the-odd-natural-numbers-is-1-1-1-3-4-1-3-5-9-1-3-5-7-16-1-3-5-7-9-25-show-that-from-this-result-i-1-n-2i-1-n-2-

Question Number 94096 by Rio Michael last updated on 16/May/20 $$\mathrm{The}\:\mathrm{result}\:\mathrm{of}\:\mathrm{adding}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{is}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{1}\:+\:\mathrm{3}=\mathrm{4} \\ $$$$\:\:\mathrm{1}\:+\:\mathrm{3}+\:\mathrm{5}\:=\:\mathrm{9} \\ $$$$\mathrm{1}\:+\:\mathrm{3}\:+\:\mathrm{5}\:+\mathrm{7}\:=\:\mathrm{16} \\ $$$$\mathrm{1}\:+\:\mathrm{3}\:+\:\mathrm{5}\:+\:\mathrm{7}+\mathrm{9}\:=\:\mathrm{25} \\ $$$$\:\mathrm{show}\:\mathrm{that}\:\mathrm{from}\:\mathrm{this}\:\mathrm{result},\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\mathrm{2}{i}−\mathrm{1}\right)\:=\:{n}^{\mathrm{2}}…

Question-28456

Question Number 28456 by mondodotto@gmail.com last updated on 26/Jan/18 Commented by Tinkutara last updated on 26/Jan/18 5 Answered by Rasheed.Sindhi last updated on 26/Jan/18 $$\mathrm{f}\left(\mathrm{2}\right)=\mathrm{5},\mathrm{f}\left(\mathrm{3}\right)=\mathrm{4},\mathrm{g}\left(\mathrm{2}\right)=\mathrm{5},\mathrm{g}\left(\mathrm{3}\right)=\mathrm{2},\mathrm{g}\left(\mathrm{4}\right)=\mathrm{1}…

Question-159491

Question Number 159491 by akolade last updated on 17/Nov/21 Answered by Tokugami last updated on 18/Nov/21 $$\int_{\mathrm{0}} ^{\:\frac{{d}}{{dx}}\int_{\mathrm{0}} ^{\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{e}^{−{x}} \underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{k}} }{{k}!}} \pi\:{dt}}…