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2d
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 ...
2d
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 ?
Jan
23
accepted $\sum_1^\infty{\frac{(-1)^n}{\ln{(2\cosh{n})}}}$ convergence
Jan
23
asked Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$
Jan
22
awarded  Yearling
Jan
22
revised $\sum_1^\infty{\frac{(-1)^n}{\ln{(2\cosh{n})}}}$ convergence
added 61 characters in body
Jan
22
comment $\sum_1^\infty{\frac{(-1)^n}{\ln{(2\cosh{n})}}}$ convergence
Yes but for absolute ?
Jan
22
asked $\sum_1^\infty{\frac{(-1)^n}{\ln{(2\cosh{n})}}}$ convergence
Jan
22
asked Test convergence of $\sum_{n=2}^\infty{(\ln{n})^{-n}}$
Jan
21
comment $\sum_1^{\infty}\frac{\ln(n)}{n^{5/2}}$ and Cauchy condesation test
$ln(n)<n$ would work too ?
Jan
21
comment $\sum_1^{\infty}\frac{\ln(n)}{n^{5/2}}$ and Cauchy condesation test
cauchy series should start from zero ?