15) 2 +6 + 8 + 10 + ...

Infinite geometric series:

Condition 1:

An infinite geometric series converges if and only if ''the value of common ratio is less than 1'' ( r <1). In this case, sum of the series is equal to a₁/(1-r) where a₁ is the first term and r is the common ratio.

Condition 2: 

An infinite geometric series diverges if the value of common ratio is more than 1 ( r >1). In this case, sum of the series 

has no limit and the sum approaches infinity.

Infinite arithmetic series:

The sum of an infinite arithmetic series is either +∞, if d=positive, or - ∞, if d=negative where d is common difference.

Because the sum of infinite arithmetic series approaches infinity, therefore the infinite arithmetic series diverges.

Any other series: 

If the sum of any series approaches infinity then the series diverges.