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Category: Arithmetic

Show-that-5-21-8-55-7-33-6-35-

Question Number 582 by ssahoo last updated on 31/Jan/15 $$\mathrm{Show}\:\mathrm{that} \\ $$$$\sqrt{\mathrm{5}+\sqrt{\mathrm{21}}}\:+\sqrt{\mathrm{8}+\sqrt{\mathrm{55}}}\:=\sqrt{\mathrm{7}+\sqrt{\mathrm{33}}}\:+\sqrt{\mathrm{6}+\sqrt{\mathrm{35}}} \\ $$ Commented by prakash jain last updated on 31/Jan/15 $$\sqrt{\mathrm{5}+\sqrt{\mathrm{21}}}={a}+{b} \\ $$$${a}^{\mathrm{2}}…

Question-66036

Question Number 66036 by aliesam last updated on 08/Aug/19 Answered by mr W last updated on 08/Aug/19 $$=\mathrm{2}\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\frac{{n}}{\mathrm{2}}\right) \\ $$$$=\mathrm{2}×\frac{\left(\mathrm{1}+\frac{{n}}{\mathrm{2}}\right)\frac{{n}}{\mathrm{2}}}{\mathrm{2}} \\ $$$$=\frac{{n}\left({n}+\mathrm{2}\right)}{\mathrm{4}} \\ $$ Terms…