Sequences
Sum to infinity, when it converges
As n grows, r^n tends to zero, so the finite formula collapses to this. Outside that condition there is no limit to quote.
The Formula
S-infinity = a1 / (1 - r), valid only for |r| < 1
As n grows, r^n tends to zero, so the finite formula collapses to this. Outside that condition there is no limit to quote.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| |r| | Absolute ratio | dimensionless | Strictly below 1 for convergence. Equal to 1 or above means divergence. |
What Each Symbol Means
|r|dimensionless
Absolute ratio
Strictly below 1 for convergence. Equal to 1 or above means divergence.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to find the sum of a geometric series page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Find The Sum Of A Geometric Series, filed under Math. Every number the guide produces comes from substituting into this one line.