Question

Does the following infinite series converge or diverge? 3/2 + 12/2 +48/2 +192/2

diverges, has a sum
converges, has a sum
diverges, doesn't have a sum
converges, doesn't have a sum

Answer 1

diverges to infinity

Explanation:

This is the same as:
`3/2+6+24+96+...`

By observation each successive term is greater than the previous so the sum is always increasing. As it is an infinite series the sum must eventually reach infinity.

So the sum is infinity `->oo`

Some would argue that it does not have a sum as infinity is not measurable. On the other hand I have come across the phrase 'sums to infinity'. So I am not sure if you could or could not describe this as: "diverges, has a sum"