# Convergent or divergent series

Use the ratio a_n/a_(n+1) to determine if the following sequences are monotonic increasing, decreasing or neither.

Use the derivative test to determine if the following sequences are monotonic increasing, decreasing or neither.

Use the nth term test to stae if the series converges, diverges, or cannot tell.

Use the integral test to determine if the series converges or diverges

Use the comparison test test to determine if the series converges or diverges

Use the limit comparison test with the dominant term concept to determine if the series converges or diverges

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#### Solution Preview

1. Use the ratio to determine if the following sequences are monotonic increasing, decreasing or neither.

Solution:

We can't say whether the term is less than 1 or greater than 1.

Thus the given series neither increasing nor decreasing.

2. Use the derivative test to determine if the following sequences are monotonic increasing, decreasing or neither.

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#### Solution Summary

This posting explains different methods of testing convergent or divergent series.