Question

Determine if the following infinite geometric series converges or diverges. If it converges, use the formula to find the sum. If it diverges, explain why you cannot find the sum. a1 = 7 and r = 5/2 Find S

Answer 1

A geometric series with a common factor r is convergent if the absolute value of r is less than 1.

In this case, the common factor is 5/2, which is greater than 1.

Therefore, the described series diverges.

We cannot find the sum of a divergent series because the value of the sum eventually overcomes any number, no matter how big it is.