Conditional convergence

In mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely.

More precisely, a series ${\displaystyle \scriptstyle \sum \limits _{n=0}^{\infty }a_{n}}$ is said to converge conditionally if ${\displaystyle \scriptstyle \lim \limits _{m\rightarrow \infty }\,\sum \limits _{n=0}^{m}\,a_{n}}$ exists and is a finite number (not ∞ or −∞), but ${\displaystyle \scriptstyle \sum \limits _{n=0}^{\infty }\left|a_{n}\right|=\infty .}$

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