Alternating Series Test Calculator

About this calculator

The alternating series test (Leibniz test) is a convergence test from calculus for series whose terms alternate in sign, such as Σ(−1)ⁿ⁺¹/nᵖ. It states that if the absolute value of the terms, bₙ = 1/nᵖ here, decreases monotonically toward zero as n grows, then the alternating series converges — a much easier condition to check than the general convergence tests needed for series without alternating signs. A useful bonus is the error bound: truncating the series after N terms leaves a remainder no larger in absolute value than the first omitted term, b_(N+1).

This calculator checks that monotonic-decrease-to-zero condition for a chosen exponent p, reports whether the alternating p-series converges by the Leibniz test, and computes the partial sum of the first N terms so you can see how quickly it’s approaching its limit — standard material in an introductory real-analysis or calculus II course on series convergence.