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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 Ratio Test: All terms are positive and ____1forallk1

Short Answer

Expert verified

The required answer isak+1ak1forallk1

Step by step solution

01

Step 1. Given Information

The given term is ratio test.

02

Step 2. Explanation

The ratio test follows from the fact that a fraction abis greater than or equal to 1 exactly when the numerator is greater than or equal to denominator.

Thus,ak+1ak1forallk1

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