One way to to characterize a geometric series is that the ratio between successive terms is constant. That is, b„ = r" for all n E N (i.c., E bn is a geometric series) if and only if bo = 1 and nil =r for all n E N. We also know that a geometric series " converges if and only if |r| < 1. Given some series an, if we know that lim dni = L < 1, then eventually "nil is bounded above by some number less than 1, and in turn a, is eventually bounded above by a convergent geometric scries. Then Ca,n converges by the BCT with that geometric series.
One way to to characterize a geometric series is that the ratio between successive terms is constant. That is, b„ = r" for all n E N (i.c., E bn is a geometric series) if and only if bo = 1 and nil =r for all n E N. We also know that a geometric series " converges if and only if |r| < 1. Given some series an, if we know that lim dni = L < 1, then eventually "nil is bounded above by some number less than 1, and in turn a, is eventually bounded above by a convergent geometric scries. Then Ca,n converges by the BCT with that geometric series.
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 25RE: Use the formula for the sum of the first nterms of a geometric series to find S9 , for the series...
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just need answer for part d and part e, pls
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