∑n=0∞an,an=1⋅(0.5)n
Sequences & Series tool
Series convergence tester
Pick a shape and its parameters, and watch the real test — ratio test or p-series test — get applied step by step, with the actual limit computed.
Verdict: Converges
Step 1 / 4The series
Common questions
Which convergence tests does this use?
The ratio test for the geometric, power-over-exponential and factorial shapes, and the standard p-series test for 1/nᵖ. Both are worked out with the actual limit, not just a stated rule.
Why can't I type my own series?
Free-text formula parsing can silently misread what you typed. Picking a shape and its parameters means every input is unambiguous, so the tool can never quietly compute the wrong series.
Does a converging series always have a computable sum shown?
Only the geometric case has a simple closed-form sum, so that's the one shown when it converges. The other tests establish convergence or divergence, not the sum.