Does the following infinite geometric series diverge or converge? Explain.
7 + 21 + 63 + 189 + . . .
To determine whether the given infinite geometric series converges or diverges, we must first find the common ratio, r.
We notice that each term in the series is obtained by multiplying the previous term by the same value, which is 3.
So, the common ratio, r, is 3.
For an infinite geometric series to converge, the absolute value of the common ratio must be less than 1. In this case, |3| = 3, which is greater than 1.
Therefore, the given infinite geometric series diverges.