Final answer:
The series is divergent because the common ratio's absolute value is greater than 1.
Step-by-step explanation:
The series 1 - 5/4 + 25/16 - 125/64 + 635/256 is an example of a geometric series, where each term after the first is found by multiplying the previous term by a common ratio. In this case, the common ratio is -5/4.
A geometric series converges if the absolute value of the common ratio is less than 1.
Since |-5/4| > 1, the series diverges and does not have a sum.