Ben H.

asked • 07/17/15

How does Sn = 1 + t + t^2 + ... + t^(n-1) = (1-t^n)/(1-t)?

The original question is "show that if t∈R with modulus of t < 1, then the series ∑n=1inf tn-1= 1+t+t2+... coverges.

1 Expert Answer



The series can also be regarded as a converging Geometric Series, because t < 1. The sum of such an infinite series is a1/(1 - r). In this case, a1 = 1 and r = t. From the result above, as n → inf, tn → 0, so we end up with 1/(1 - t)


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