Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If an answer does not exist, enter DNE.) 1 + 0.5 + 0.25 + 0.125 + ...

Convergent. The sum is 2.

Step-by-step explanation:

First let's find the rate of the series. We can find it by dividing one term by the term before:

So the rate of the series is 0.5. The series is convergent if the rate is between 0 and 1, so this series is convergent.

We can find its sum with the following equation:

Where a_1 is the first term and r is the rate.

So we have that:

The sum of the series is 2.

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.