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Chapter 12: Q. 37 (page 816)

Find each sum.

1 + 3 + 5 + ... + (2n - 1)

Short Answer

Expert verified

The sum of the given sequence isn2.

Step by step solution

01

Step 1. Given information

Thegivensequenceis1+3+5+...+2n−1

We have to find the sum of the sequence.

02

Step 2. calculating the sum

Thesumofthearithmeticsequenceisgivenas⇒Sn=na1+an2Wehave,a1=1an=2n−1Thus,⇒Sn=n1+2n−12=n2n2=n2

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Most popular questions from this chapter

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.

a1=5;an=2an-1

In Problems 51–60, write out each sum.

∑k=2n-1kInk

In Problems 17–28, write down the first five terms of each sequence.

sn=n

In Problems 17–28, write down the first five terms of each sequence.

an=nn+2

In Problems 51–66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

∑k=1∞813k-1
See all solutions

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