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The series  is

  1. Convergent
  2. Divergent
  3. Oscillatory
  4. None of these

Answer (Detailed Solution Below)

Option 2 : Divergent
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Detailed Solution

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Concept:

The comparison test in the limit form,

Consider two positive term series  and  such that  (finite), then both the series either converge or diverge.

Calculation:

Given series is

⇒ 

Lets take  

By comparison test in limit form,

Therefore, both the series either converge or diverge.

The series ∑bn is a geometric progression with r = 2.5, since r > 1, series is divergent.

As bn is divergent, an is also divergent.

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