In the lecture we saw that the sum of the infinite series 1+x + x² + • · equals .. 1/(1 – x) as long as x < 1. In this problem, we will derive a formula for summing the first n +1 terms of the series. That is, we want to calculate Sn 1+ x + x² + + x" .. The strategy is exactly that of the algebraic proof given in lecture for the sum of the full geometric series: compute the difference sn xSn and then isolate sn. What formula do you get?

In the lecture we saw that the sum of the infinite series 1+x + x² + • · equals .. 1/(1 – x) as long as x < 1. In this problem, we will derive a formula for summing the first n +1 terms of the series. That is, we want to calculate Sn 1+ x + x² + + x" .. The strategy is exactly that of the algebraic proof given in lecture for the sum of the full geometric series: compute the difference sn xSn and then isolate sn. What formula do you get?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

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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