How do i solve this problem?

if a number is divisible by 2, then it is even. the number 14 is divisible by 2.

It every number divisible by 2 is even then since 14 is divisible by 2 you know 14 must be even

The only general answer is to say that by checking that as more terms of the series are added, the partial sum of all those terms converges. It does not need to have a geometric convergence, so unfortunately you can't use the ratio os the geometric series. If your series were only geometric, then yes, if |r|<1. But in general, only if the partial sums are convergent, that is if the more terms you add, the result changes closer and closer to zero.

It can be written mathematically, such that there exists a term k for which the sum from k to infinity is bounded, but you may not need all the jargon.

Again, make sure there was not an assumption about a specific type of series, like geometric, which is the one considered in the other answer