# Does #a_n=(-1/2)^n# sequence converge or diverge? How do you find its limit?

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Does #a_n=(-1/2)^n# sequence converge or diverge? How do you find its limit?

Does

##### 1 Answer

Dec 21, 2017

Sequence converges.

#### Explanation:

Let's look at a few terms of this sequence.

This is a geometric progresion (GP) with first term

We are asked whether or not the sequence converges.

Consider,

Now let's consider the sum of the infinite series

The sum of an infinite GP where

Hence, in our example:

So, we can state that the sequence converges and the sum of the infinite sequence converges to