2021-11-26, 14:13 | #1 |
"Matthew Anderson"
Dec 2010
Oregon, USA
48F_{16} Posts |
geometric series
Many 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 Wikipedia 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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