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Determine whether the series j=22j3converges or diverges. Give the sum of the convergent series.

Short Answer

Expert verified

The seriesj=22j3diverges.

Step by step solution

01

Step 1. Given information.

Given a series j=22j3.

02

Step 2. Find if the series converges or not.

The index starts with 2, rather than 0.

Note that the convergence of a series depends not upon the first few terms but only upon the tail of the series.

The standard form of a geometric series is k=0crk.

The geometric series converges if and only if r<1.

Here, the series j=22j3has c=13and r=2.

Since r=2, it follows that the series j=22j3diverges.

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