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Jan
26
accepted Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$
Jan
26
comment Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$
yes I am sure...
Jan
26
comment Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$
Sorry but without this
Jan
26
asked Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$
Jan
26
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)
Jan
26
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.
Jan
26
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...
Jan
26
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 $|a_k|^2$?
Jan
26
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|)$?
Jan
26
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 ...
Jan
26
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.
Jan
25
asked Limit $\lim \limits_{x\to0}{\frac{\ln(x+1)}{2^x-1}}$ wihout LHospital
Jan
23
accepted Convergence of $\sum_{n=1}^\infty{\frac{\ln({3n^2 +4n+5})}{n^{4/3}}}$
Jan
23
asked Convergence of $\sum_{n=1}^\infty{\frac{\ln({3n^2 +4n+5})}{n^{4/3}}}$
Jan
23
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
Jan
23
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
Jan
23
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 ?
Jan
23
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 $n>N$
Jan
23
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 $1/a_n^r$
Jan
23
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 ?