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Chapter 7: Q. 1 (page 655)

Fill in the blanks to complete each of the following theorem statements.

Tests for Monotonicity: A sequence {ak} is increasing if it passes any of the following tests:

The Difference Test: _____鈮�0forallk鈮�1

Short Answer

Expert verified

The required answer isak+1-ak鈮�0forallk鈮�1

Step by step solution

01

Step 1. Given Information

The given term is difference test.

02

Step 2. Explanation

The sequence ak+1-ak鈮�0forallk鈮�1making the sequence an increasing sequence.

Thus, the difference test follows directly from the definition of monotonicity.

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Most popular questions from this chapter

Leila, in her capacity as a population biologist in Idaho, is trying to figure out how many salmon a local hatchery should release annually in order to revitalize the fishery. She knows that ifpksalmon spawn in Redfish Lake in a given year, then only 0.2pkfish will return to the lake from the offspring of that run, because of all the dams on the rivers between the sea and the lake. Thus, if she adds the spawn from h fish, from a hatchery, then the number of fish that return from that run k will be pk+1=0.2(pk+h)..

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