?How do you find the sum of the infinite geometric series 4, 7, 12.25, 21.4375 …?
The series diverges.
Without even considering that it is a geometric series, we can see that the sequence is increasing, and thus its sum will necessarily increase without bound.
For a geometric series
with initial term
A derivation of this formula, along with more information on geometric series, may be found here,
As an aside, we can look at the given series and find that