Changes

:<math>\lim_{N\rightarrow\infty}\sum^{N}_{n=1}a_{n}=L</math>

:<math>\lim_{N\rightarrow\infty}\sum^{N}_{n=1}a_{n}=L</math>

for <math>L</math> a finite number, <math>|L|<\infty</math>. It will occur only if (<math>\Leftarrow</math>),

for <math>L</math> a finite number, <math>|L|<\infty</math>. The terms in the limit are known as [[partial sum]]s. If the partial sums approach <math>\infty</math> or <math>-\infty</math>, the series is said to '''diverge'''. If the partial sums do not approach a single value, finite or infinite, then the series is said to have no limit.

 

Convergence of the series will occur only if (<math>\Leftarrow</math>),

:<math>\lim_{n\rightarrow\infty}a_{n}=0</math>

:<math>\lim_{n\rightarrow\infty}a_{n}=0</math>