In mathematics, an alternating series is an infinite series of the form {\displaystyle \sum _{n=0}^{\infty }^{n}a_{n}} or {\displaystyle \sum _{n=0}^{\infty }^{n+1}a_{n}} with aₙ > 0 for all n. The signs of the general terms alternate between positive and negative.
What is meant by alternating series?
In mathematics, an alternating series is an infinite series of the form or. with an > 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.
How do you determine if a series is alternating?
The Alternating Series Test
If a[n]=(-1)^(n+1)b[n], where b[n] is positive, decreasing, and converging to zero, then the sum of a[n] converges. With the Alternating Series Test, all we need to know to determine convergence of the series is whether the limit of b[n] is zero as n goes to infinity.
