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Chapter 7: Q. 40 (page 615)

Evaluate the finite sums.

鈭�j=1603j

Short Answer

Expert verified

On evaluating, we get,

3360-13-1

Step by step solution

01

Step 1. Given information.

Consider the given question,

鈭�j=1603j

02

Step 2. Use the sum of n terms of geometric series.

The geometric series 鈭�j=1603jin the expanded form is 鈭�j=1603j=3+32+33+...+360.

The series has the first term a=1.

The common ratio r=3with no. of terms,

n=60

The finite sum of the geometric series with ratio greater than 1, localid="1649266007528" Sn=arn-1r-1.

Substituting the values,

S60=3360-13-1

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Most popular questions from this chapter

In Exercises 48鈥�51 find all values of p so that the series converges.

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0.237237237...

Find the values of x for which the series 鈭�k=0鈭�cosx2kconverges.

Express each of the repeating decimals in Exercises 71鈥�78 as a geometric series and as the quotient of two integers reduced to lowest terms.

0.6345345...

Determine whether the series 鈭�k=0鈭�-98kconverges or diverges. Give the sum of the convergent series.
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