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 Dec31 awarded Nice Answer Dec14 answered Convergence of series involving iterated $\sin$ Oct15 awarded Yearling Nov2 awarded Necromancer Oct15 awarded Yearling Sep7 comment How may I prove this inequality? Someone calls this method "uvw" downloadable here artofproblemsolving.com/Forum/… Sep7 answered Compute $\int_{0}^{1}\frac{\ln(x) \ln^2 (1-x)}{x} dx$ Sep2 comment proving :$\frac{(ab+b)(2b+1)}{(ab+a)(5b+1)}+\frac{(bc+c)(2c+1)}{(bc+b)(5c+1)}+\frac{(ca+a)(2a+1)}{(ca+c)(5a+1)}\ge\frac{3}{2}$ It comes from here fen.bilkent.edu.tr/~cvmath/Problem/problem_2011.htm (April 2011) Aug30 answered Inequality $(a+\frac{1}{b})^2+(b+\frac{1}{c})^2+(c+\frac{1}{a})^2\ge 16$ Jun21 answered Linear change of variables in Hamiltonian functions Jun19 answered Question on sequences Jun19 answered infinite series involving harmonic numbers and zeta Jun14 answered Calculate alpha from $\alpha + \sin(\alpha)$ = K Jun14 comment An inequality involving integrals @Mohamed: <<....function $x↦6x−2=3(2x−1)$ used...>>?? Jun14 awarded Supporter Jun14 answered An inequality involving integrals Jun14 comment Convergence of a function series The general term may well be not positive: put a minus sign in front of the series. As for the monotonicity, note that $$\left(\frac 1t\ln \frac xt\right)' =\frac{\ln t}{t^2} -\frac{1+\ln x}{t^2}$$ so is asymptotically incresing. The assumption are satisfied except at most for a finite number of terms but this doesn't affect the convergence Jun13 answered Convergence of a function series Jun12 answered Computing $\sum_{n=0}^{\infty} u_{n}, \frac{u_{n+1}}{u_n}=\frac{n+a}{n+b}$ Jun9 revised abel summable implies convergence deleted 25 characters in body