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Chapter 7: Q. 59 (page 592)

In Exercises 59鈥�62 use the derivative test in Theorem 7.6 to analyze the monotonicity of the given sequence.

k+1k

Short Answer

Expert verified

The given sequence is strictly decreasing.

Step by step solution

01

Step 1. Given Information.

The given sequence isk+1k.

02

Step 2. Use the derivative test.

To analyze the monotonicity of the given sequence we will use the derivative test.

Let the function is f(k)=k+1k.

According to the derivative test,

f'(k)=k12k+1-k+1k2f'(k)=k-2k+12k+1k2f'(k)=k-2k-2k22k+1f'(k)=-k-2k22k+1f'(k)=-k+2k22k+1

Now, f'k<0forallk>0.

Therefore, the given sequence is strictly decreasing.

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