Calculus Examples

Determine Convergence with the Integral Test
Step 1
To determine if the series is convergent, determine if the integral of the sequence is convergent.
Step 2
Write the integral as a limit as approaches .
Step 3
The integral of with respect to is .
Step 4
Simplify the answer.
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Step 4.1
Evaluate at and at .
Step 4.2
Remove parentheses.
Step 4.3
Use the quotient property of logarithms, .
Step 5
As log approaches infinity, the value goes to .
Step 6
Since the integral is divergent, the series is divergent.
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