Series Convergence Calculator
series convergence calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed by Manoj Kumar, Mathematics Educator
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Ratio Test: L = |a(n+1)/a(n)| → if L<1 converges, L>1 diverges, L=1 inconclusive
Tests for series convergence: Ratio test computes the limit of consecutive term ratios. Also checks: partial sums trend, term magnitude approaching zero (necessary condition), and root test.
Worked Examples
Example 1: Geometric series 1/2^n
Problem:a(n) = 1/2^n, starting at n=1
Solution:Ratio = 0.5 < 1, converges. Sum = 1/(1-0.5) = 1 (starting at n=0) or 1 (starting at n=1)
Result:Converges. Partial sum → 1.0
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy