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Determine whether the series 9940-9920+9910-995+converges or diverges. Give the sum of the convergent series.

Short Answer

Expert verified

The series 9940-9920+9910-995+diverges.

Step by step solution

01

Step 1. Given information.

Given a series 9940-9920+9910-995+.

02

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 role="math" localid="1648983721211" 9940-9920+9910-995+it can be seen that c=9940.

Every term after that is -2times the previous term.

It follows that r=-2.

Since r=-2, the series 9940-9920+9910-995+diverges.

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