Series

[vague crystal]

Does anyone know what tests to use for these when determining convergence or divergence

[tropic haven]

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[verbal ermine]

For the first one, you can use : $\sum u_n -> l => u_n -> 0$
And for the second : $\sum |u_n| -> l => \sum u_n cv$
You can check out the Cauchy-Hadamard theorem if you want to learn more 😉

[manic schooner]

Heolorus

[prime beacon]

for the bottom summation, use the fact that the series absolutely converges to show that it must converge.
for the top summation,
use the fact that n^3-1/n^3+n+1 has a limit of 1 and not 0 as n tends to infinity, hence it must diverge.

[verbal ermine]

use what i said in fact 🤓

[prime beacon]

what even is u_n