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Chapter 7: Q. 52 (page 592)

In Exercises 51–54 use the difference test in Theorem 7.6 to analyze the monotonicity of the given sequence.

k-k+1

Short Answer

Expert verified

The given sequence is strictly decreasing fork≥1.

Step by step solution

01

Step 1. Given Information.

The given sequence isk-k+1.

02

Step 2. Use the difference test. 

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

Let the general term of the sequence isak=k-k+1.

So, the term ak+1is

ak+1=k+1-k+1+1.

According to the test,

role="math" localid="1649229948859" ak+1-akk+1-k+2-k-k+1k+1-k+2-k+k+12k+1-k+2-k

Now, ak+1-ak<0forallk≥1.

Thus, the sequence is strictly decreasing fork≥1.

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