1- sum of n=1 to infinity (6+2^n-1)/(3^n-2) determine if the series converges or diverges

2-sum of n=1 to infinity (n^e)/(n^pi) determine if the series converges or diverges

3- sum of n=1 to infinity (n)/(2n^2-1) determine if the series converges or diverges

4-If sum of n=1 to infinity (an + bn) converges do sum of n=1 to infinity an and sum of n=1 to infinity bn converge as well? Give an example showing this doesn't always happen and make sure you explain why your example works.