Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 11 - Section 11.2 - Arithmetic Sequences - Exercise Set - Page 842: 89


Hence, proved. $S_n=n^2$.

Work Step by Step

The given sequence is $1+3+5+....+(2n-1)$. This is the arithmetic series. Common difference $d=2$. First term $a=1$. Last term $l=(2n-1)$. Number of terms $n$. Sum of all terms is $\frac{n}{2}\cdot (a+l)$. Substitute all values. $=\frac{n}{2}\cdot (1+(2n-1))$ Simplify. $=\frac{n}{2}\cdot (1+2n-1)$ $=\frac{n}{2}\cdot (2n)$ $=n^2$.
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