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Chapter 7: Q. 60 (page 592)

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

k2-k

Short Answer

Expert verified

The given sequence is strictly increasing.

Step by step solution

01

Step 1. Given Information.

The given sequence isk2-k.

02

Step 2. Use the derivative test. 

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

Let the function isf(k)=k2-k.

According to the derivative test,

f'(k)=2k-1

Now, f'(k)>0forallk>0.

Therefore, the given sequence is strictly increasing.

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