For questions related to alternating expression (or series). It is a sequence, whose terms change sign (i.e. if a term $a_n$ is positive then $a_{n+1}$ is negative and vice versa).
Basically, alternating sequence is a sequence, whose term change sign (i.e. if a term $a_n$ is positive then $a_{n+1}$ is negative and vice versa).
It is an infinite series of the form $\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}$ or $\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}$ with $a_n > 0$ for all $n$.
The signs of the general terms alternate between positive and negative. Like any series, an alternating series converges if and only if the associated sequence of partial sums converges.
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