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 Jan26 accepted Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$ Jan26 comment Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$ yes I am sure... Jan26 comment Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$ Sorry but without this Jan26 asked Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$ Jan26 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ I have solutions which are fine but are not acceptable from professor. (I study computer science) Jan26 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ Yes it is pointless. However in case I get a solution I'll share it. Jan26 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ I dont know he didnt tell me.Maybe he is going to tell me but I am not sure if he will. In case I'll post it. I'll show him this again... Jan26 comment How to prove that if $\sum_{n=0}^{\infty}a_n$ absolutely convergent $\Rightarrow \sum_{n=0}^{\infty}(a_n)^2$ convergent why does sum raised at power is larger than $|a_k|^2$? Jan26 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ did you figured out randomly the $a_n^2 \leq |a_n|(\sum_1^\infty|a_n|)$? Jan26 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ phd professor told me that this is really poor and unacceptable ... Jan26 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ teacher told me that this is poor proof and not valid and that there is simpler one. Jan25 asked Limit $\lim \limits_{x\to0}{\frac{\ln(x+1)}{2^x-1}}$ wihout LHospital Jan23 accepted Convergence of $\sum_{n=1}^\infty{\frac{\ln({3n^2 +4n+5})}{n^{4/3}}}$ Jan23 asked Convergence of $\sum_{n=1}^\infty{\frac{\ln({3n^2 +4n+5})}{n^{4/3}}}$ Jan23 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ So direct comparison doesnt necesarily mean something for their sums (comparison) ,interesting .eg $\sum _{n=1}^{\infty } \left(\frac{100}{n^2}\right)^2$ > $\sum _{n=1}^{\infty } \left(\frac{1}{n^2}\right)$ . thanks Jan23 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ My problem is that in case $a_n$ in the beginning before $a_n$<1 ,$a_n^2$ is way larger and produce a bigger sum Jan23 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ @Syuizen how did you come up with the inequality ? Jan23 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ great explanation. however it seems that there should be a $n>N$ Jan23 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ it doesnt hold .But how do harmonic series relate? they are $1/n^r$ not $1/a_n^r$ Jan23 comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ Ok but why this inequality is true ?