10:39 AM
@user153330 Does searching for $\sum x_ny_n<\infty$, $\lim_{n\to\infty} y_n=\infty$ give some results similar to what you want?
in Mathematics, 18 hours ago, by user153330
hi yall! having a bit of trouble proving something from real analysis. so assume u have a sequence $x_n>0$ such that $\sum x_n$ converges. now i need to prove that there exists another sequence $y_n>0$ such that $\sum x_ny_n$ converges and $y_n$ goes to infinity. the best i could do is to reframe the problem as showing that must exist some $y_n>0$ such that $\sum x_ny_n$ is bounded and $y_n\to+\infty$, but I don't know how to attack it. i'd appreciate any hint

hello Martin, haha u were faster than me x)
yes that was useful, but i do wonder why my query didn't work:
https://approach0.xyz/search/?q=%24%5Csum_%7Bk%3D1%7D%5E%5Cinfty%20x_ny_n%24%2C%20converge%2C%20%24%5Csum_%7Bk%3D1%7D%5E%5Cinfty%20x_n%24&p=1

I am not really sure what you mean by "didn't work". The query you linked returned posts which contain the term you entered in the search field.
Is it possible that the result would be better if you used the same variable in the sum and in the index?
I.e. writing $\sum_{k=1}^\infty x_k$ rather than $\sum_{k=1}^\infty x_n$.
One can try many various versions to enter into the search field.
I'll have to go. See you later!

@MartinSleziak sorry that was my mistake
@MartinSleziak so in this case it seems better keywords were the key, i don't have much experience with approach0 so thanks for your help!

it doesn't seem like approach0 is at fault with that previous search query, and it did find what i was looking for in your query, so problem solved