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?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

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?

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