quartz/content/Obsidian Vault/Alternating Series Test.md

#math/calculus

another freaking test for convergence/divergence of a series

apparently even \sum\limits \frac{1}{n} converges when it's alternating. Just take out the (-1)^{n}.

procedure

take out the (-1)^{n}, and you're left with b_{n}, if \lim_{n->\infty} b_{n} = 0, and b_{n+1}\leq b_n for all n, then the whole series converges.

absolute vs conditional convergence

error

edek: !