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Chapter 7: Q. 10 (page 624)

What is meant by the remainder Rn of a series 鈭�k=1鈭�ak

Short Answer

Expert verified

The remainder of the series 鈭�k=1鈭�ak is Rn=鈭�k=n+1鈭�ak.

Step by step solution

01

Step 1. Given Information.

The series:

鈭�k=1鈭�ak

02

Step 2. The remainder of the convergent series.

If 鈭�k=1鈭�ak is a convergent series with sum L, then we may approximate L with the nth partial sum Sn=鈭�k=1nak. The nth remainder is defined by

Rn=L-Sn=鈭�k=n+1鈭�ak

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Most popular questions from this chapter

Determine whether the series 鈭�k=0鈭�e蟺3kconverges or diverges. Give the sum of the convergent series.

Given that a0=-3,a1=5,a2=-4,a3=2and 鈭�akk=2鈭�=7, find the value of鈭�akk=0鈭�.

Determine whether the series 鈭�k=0鈭�蟺e3kconverges or diverges. Give the sum of the convergent series.

Given thata0=-3,a1=5,a2=-4,a3=2and鈭�akk=2鈭�=7, find the value of鈭�akk=4鈭�.

Use either the divergence test or the integral test to determine whether the series in Exercises 32鈥�43 converge or diverge. Explain why the series meets the hypotheses of the test you select.

36.鈭�k=1鈭�kk2+3
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