Conditional Convergence and Series Tests

Math actually breaks if you rearrange the wrong infinite list of numbers. This is the dark

side of calculus called conditional convergence. To survive this, you need a toolkit

of tests. First, the Comparison Test is your best friend—just check if your messy

equation behaves like a simple one you already know. If you see factorials or exponentials,

drop everything and use the Ratio Test. If the limit is less than one,

you win. But remember, unless it’s absolutely convergent, changing the order

of the numbers can change the final answer to literally anything.