Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Abstract Algebra: An Introduction
Found in: Page 528
Abstract Algebra: An Introduction

Abstract Algebra: An Introduction

Book edition 3rd
Author(s) Thomas W Hungerford, David Leep
Pages 608 pages
ISBN 9781111569624

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Let r be a real number, r1. Prove that for every integer n1 , 1+r+r2+r3+....+rn-1=rn-1r-1


It is proved that for every integer n1:


See the step by step solution

Step by Step Solution

Consider the given parameters

Assume that r1 is a real number. The objective is to show that for each integer n1 .


Obtain the equation for Sr

Let S=1+r+r2+r3+...+rn-1 …. (1)

Then multiply both the sides of the sum S by the real number r and get the equation as follows:

role="math" localid="1648726203258" Sr=r1+r+r2+r3+....rn-1Sr=r+r2+r3+.....+rn-1+rn.....(2)

Solve the equations (1) and (2)

Subtract equation (1) from equation (2) and solve in the following manner:


S=1+r+r2+r3+....+rn-1; therefore, 1+r+r2+r3+.......+rn-1=rn-1r-1 .

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.