Question

Determine whether the geometric series 25 − 5 + 1 − 0.2 ... converges or diverges, and identify the sum if it exists.

Answer 1

Answer:

Converges

Sum = 20.8333

Step-by-step explanation:

A geometric series has a general formula of:

$\sum ar^n$

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:

$\sum 25*(-0.2)^n$

Since 0.2 < 1.0, the series converges.

The sum of the series is given by:

$S=\frac{a}{1-r}\\S=\frac{25}{1-(-0.2)}\\S=20.8333$

The sum is 20.8333.