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Q 50.

Found in: Page 615


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Determine whether the series n=4411n converges or diverges. Give the sum of the convergent series.

The series n=4411n converges to 26655.

See the step by step solution

Step by Step Solution

Step 1. Given information.

Given a series n=4411n.

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 n=4411n has c=4114 and r=111.

Since r=111, it follows that the series localid="1648886017183" n=4411n converges.

Step 3. Find the value to which the series converges.

If the geometric series k=0crk converges, it converges to c1-r.

So, the series n=4411n converges to 41141-111, that is 41331 or equivalently 26655.

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