Category: Arithmetic

Question Number 22939 by selestian last updated on 24/Oct/17 Answered by ajfour last updated on 24/Oct/17 $$\left(B\right)1/8$$$$\frac{a}{1-r}=4;\frac{a^3}{1-r^3}=\frac{64}{7}$$$$\Rightarrow\:\:\frac{\mathrm{7}{a}^{\mathrm{3}} }{\mathrm{1}−{r}^{\mathrm{3}} }=\frac{{a}^{\mathrm{3}}…

Question Number 22928 by selestian last updated on 24/Oct/17 Answered by $@ty@mlastupdatedon24/Oct/17$$Let{x}^{18}=y^{21}=z^{28}=k$$$$\Rightarrow{x}={k}^{\frac{\mathrm{1}}{\mathrm{18}}} ,\:{y}={k}^{\frac{\mathrm{1}}{\mathrm{21}}} ,{z}={k}^{\frac{\mathrm{1}}{\mathrm{28}}} \…

Question Number 22923 by selestian last updated on 24/Oct/17 Answered by $@ty@mlastupdatedon24/Oct/17$$I_n=\underset{0}{\stackrel{\frac{\pi }{4}}{\int }}\tan {}^{n}x\sec {}^{2}xdx$$$${I}_{{n}} =\left[\frac{\mathrm{tan}\:^{{n}+\mathrm{1}}…

Question Number 88440 by M±th+et£s last updated on 10/Apr/20 $$prove\underset{k=1}{\sum ^{\mathrm{\infty }}}\frac{4^k-3^k}{{12}^k}=\frac{1}{6}$$ Commented by Tony Lin last updated on 10/Apr/20…

Question Number 153905 by liberty last updated on 12/Sep/21 Commented by MJS_new last updated on 12/Sep/21 $$3^3(\frac{1}{2\times 5}+\frac{1}{(2+3)(5+3)}+\frac{1}{(2+2\times 3)(5+2\times 3)}+\dots +\frac{1}{(2+11\times 3)(5+11\times 3)})$$ Answered by MJS_new last updated…