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Chapter 7: Q. 29 (page 639)

In Exercises 29鈥�34 use the ratio test to analyze whether the given series converges or diverges. If the ratio test is inconclusive, use a different test to analyze the series.

鈭�k=0鈭�5kk!

Short Answer

Expert verified

The series converges.

Step by step solution

01

Step 1. Given information.

The given series is鈭�k=0鈭�5kk!.

02

Step 2. Ratio Test.

According to the given series,

ak+1=5k+1(k+1)!ak+1ak=5k+1(k+1)!5kk!=k!5k+15k(k+1)!=5(k+1)

03

Step 3. Take limits.

On Taking limits,

limk鈫�鈭�ak+1ak=limk鈫�鈭�5(k+1)=5limk鈫�鈭�1(k+1)=5(0)=0Since,L<1,

Therefore, the series converges.

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Most popular questions from this chapter

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鈭�k=1鈭�鈥�kek
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