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Author: Tinku Tara

8-4-2-1-

Question Number 81595 by zainal tanjung last updated on 14/Feb/20 $$\mathrm{8}+\mathrm{4}+\mathrm{2}+\mathrm{1}+…..\infty= \\ $$ Commented by Tony Lin last updated on 14/Feb/20 $$\mathrm{8}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}}+\centerdot\centerdot\centerdot\right) \\ $$$$=\mathrm{8}×\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}} \\…

Let-A-B-and-C-be-the-midpoints-of-the-sides-BC-CA-and-AB-of-the-triangle-ABC-Prove-that-AA-1-2-AB-AC-

Question Number 16055 by Tinkutara last updated on 17/Jun/17 $$\mathrm{Let}\:{A}',\:{B}'\:\mathrm{and}\:{C}'\:\mathrm{be}\:\mathrm{the}\:\mathrm{midpoints}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sides}\:{BC},\:{CA}\:\mathrm{and}\:{AB}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{triangle}\:{ABC}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\overset{\rightarrow} {{AA}'}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\overset{\rightarrow} {{AB}}\:+\:\overset{\rightarrow} {{AC}}\right) \\ $$ Answered by mrW1 last…

number-of-positive-integers-a-and-b-and-c-satisfying-a-b-c-b-c-a-c-a-b-5abc-

Question Number 16053 by vpawarksp@gmail.com last updated on 17/Jun/17 $${number}\:{of}\:{positive}\:{integers}\:\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\:\boldsymbol{{and}}\:\boldsymbol{{c}}\:\boldsymbol{{satisfying}} \\ $$$$\boldsymbol{{a}}^{\boldsymbol{{b}}^{\boldsymbol{{c}}} } \boldsymbol{{b}}^{\boldsymbol{{c}}^{\boldsymbol{{a}}} } \boldsymbol{{c}}^{\boldsymbol{{a}}^{\boldsymbol{{b}}} } =\mathrm{5}\boldsymbol{{abc}} \\ $$ Commented by prakash jain last…

lim-n-k-1-n-2-k-2-1-2-k-1-2-

Question Number 147122 by mathdanisur last updated on 18/Jul/21 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {{lim}}\:\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\mathrm{2}^{\boldsymbol{{k}}} \centerdot\left(\sqrt[{\mathrm{2}^{\boldsymbol{{k}}} }]{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} \:=\:?\: \\ $$ Answered by Kamel last updated on 18/Jul/21…