Question

?How do you find the sum of the infinite geometric series 4, 7, 12.25, 21.4375 …?

Answer 1

The series diverges.

Explanation:

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
`sum_(n=0)^ooar^n`
with initial term `a` and `|r| < 1`, the sum may be evaluated as

`sum_(n=0)^ooar^n = a/(1-r)`

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
`r = (ar^1)/a = 7/4` and so `|r| >= 1`