- **MattcAnderson**
(*https://www.mersenneforum.org/forumdisplay.php?f=146*)

- - **geometric series**
(*https://www.mersenneforum.org/showthread.php?t=27358*)

geometric seriesMany of you are familiar with geometric series. Here is a little derivation of a common result.
Finite Geometric Series Let S1 = 1 + a + a^2 + ... + a^n. We multiply S1 by ‘a’ then see a*S1 = a+ a^2 + … + a^(n+1). Subtract the second equation from the first one. (1-a)*S1 = 1-a^(n+1). Therefore S1 = [1-a^(n+1)]/(1-a). We are sure of this. This result about finite geometric series is in many textbooks. The [URL="https://en.wikipedia.org/wiki/Geometric_series#Sum"]Wikipedia[/URL] on this is very good. The infinite case is another story. If S2 = 1 + b + b^2 + … is an infinite sum then S2 converges for -1<b<1. |

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