NTH TERM DIVERGENCE TEST

Consider the following infinite series.




That is, this test does not work for the given series. You may use some other appropriate test to check whether the series converges or diverges.

Important Note :

The nth term divergence test can not prove convergence of a series. This test can be used only to check whether a series diverges.

For each of the following series, apply the divergence test. If the divergence test proves that the series diverges, state so. Otherwise, indicate that the divergence test is inconclusive.

Problem 1 :

Solution :

By divergence test, we can conclude that the given series diverges.

Problem 2 :

Solution :

The divergence test is inconclusive.

Problem 3 :

Solution :

By divergence test, we can conclude that the given series diverges.

Problem 4 :

Solution :

By divergence test, we can conclude that the given series diverges.

Problem 5 :

Solution :

By divergence test, we can conclude that the given series diverges.

Problem 6 :

Solution :

When n --> , the value of sin n is oscillating between -1 and +1.

By divergence test, we can conclude that the given series diverges.

Problem 7 :

Solution :

When n --> , the value of cos n is oscillating between -1 and +1.

By divergence test, we can conclude that the given series diverges.

Problem 8 :

Solution :

When n --> , the value of tan n is oscillating between - and +.

By divergence test, we can conclude that the given series diverges.

Problem 9 :

Solution :

The divergence test is inconclusive.

Problem 10 :

Solution :

By divergence test, we can conclude that the given series diverges.

Problem 11 :

Solution :

By divergence test, we can conclude that the given series diverges.

Problem 12 :

Solution :

By divergence test, we can conclude that the given series diverges.

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