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Q 59.

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 803-203+53-512+ converges or diverges. Give the sum of the convergent series.

The series 803-203+53-512+ converges to 643.

See the step by step solution

Step by Step Solution

Step 1. Given information.

Given a series 803-203+53-512+.

Step 2. Find if the series converges or not.

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

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

In the series 803-203+53-512+ it can be seen that c=803.

Every term after that is -14 times the previous term.

It follows that r=-14.

Since r=-14, the series 803-203+53-512+ 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 localid="1648982757515" 803-203+53-512+ converges to localid="1648982761274" 8031--14, that is 643.

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