Question

diverging series * diverging series = diverging series ?

Answer 1

depends on what you mean

if \(\sum a_n\) and \(\sum b_n\) both diverge then it is possible that

\(\sum a_n b_n\) converges

Answer 2

thanks a lot

Answer 3

for a simple example take \(a_n=b_n=\frac{1}{n}\)

Answer 4

but if they diverge to infinity then the product will diverge 100% right

Answer 5

aha

Answer 6

\[\sum_{n=1}^{\infty}\frac{1}{n}=\infty\]

\[\frac{1}{n}\frac{1}{n}=\frac{1}{n^2}\]

\[\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}\]

Answer 7

so I guess there is no algebra to be made with divergence and convergence