Category: Limits

Question Number 2297 by prakash jain last updated on 14/Nov/15 $$a_0=k$$$$a_{n+1}=\frac{1}{1+a_n}$$$$\underset{n\to \mathrm{\infty }}{\lim }{a}_n=?$$ Commented by Yozzi…

Question Number 133277 by Engr_Jidda last updated on 20/Feb/21 $$useweierstrassm-testanddirichlet$$$$testtoconfirmtheuniformlycovergence$$$$ofthefollowingseriesintheinterval[0,1]$$$$a)\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{cosnx}{n^4}$$$$\left.{b}\right)\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cosnx}}{{n}^{\frac{\mathrm{8}}{\mathrm{7}}} } \…

Question Number 133114 by bemath last updated on 19/Feb/21 $$\underset{x\to \mathrm{\infty }}{\lim }{(\frac{\sqrt{{\mathrm{x}}^2-\mathrm{x}}}{\mathrm{x}}+\frac{1}{4}\sin \left(\frac{2}{\mathrm{x}}\right))}^{{\mathrm{x}}^2+\sin 3\mathrm{x}}?$$ Answered by bobhans last updated on 19/Feb/21 $${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\sqrt{{x}^{\mathrm{2}}…

Question Number 133068 by mnjuly1970 last updated on 18/Feb/21 $$\dots .advanced\dots ..calculus\dots .$$$$evaluation::\underset{k=2}{\sum ^{\mathrm{\infty }}}{(-1)}^k\left(\frac{\zeta \left(k\right)-1}{k}\right)$$$$:::\mathbf{\Phi }=\underset{k=2}{\sum ^{\mathrm{\infty }}}{(-1)}^k\frac{\zeta \left(k\right)-1}{k}$$$$\:\:\:\:\:\:\:\:\:=\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\underset{{n}=\mathrm{2}}…

Question Number 132928 by metamorfose last updated on 17/Feb/21 $$\underset{k=1}{\sum ^{+\mathrm{\infty }}}{(-1)}^{k}ln(1+\frac{1}{k})$$ Commented by Olaf last updated on 17/Feb/21 $$sorrysir,Ideletedmyanswer.$$$${it}\:{was}\:{wrong}.…