Answered: Let us consider the sum, S, of the…

Let us consider the sum, S, of the following terms: r 2 r? 3r 2r pA 2 r 3r 4 r * 2m 3 mm nr" Show that S < for n 2 1 and 0 1 i=1 (1-r)² and 0

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.2: Arithmetic Sequences And Partial Sums

Problem 6ECP: Find the sum of the integers (a) from 1 to 35 and (b) from 1 to 2N.

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Question

Let us consider the sum, S, of the following terms:
r
2 r?
3r
2r
pA 2 r
3r 4 r
* 2m 3 mm
nr"
Show that S <
for n 2 1 and 0 <r<1. [Hint: E-, iri <:
(1-r)3
for n > 1
i=1
(1-r)²
and 0 <r<1.]
N NN

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