1. use the integral test to determine whether the series is convergent or divergent: summation as n=1 to infinity of n²e^-n
2. use the integral test to determine whether the series is convergent or divergent: summation as n=1 to infinity of n/n²+1
3. use direct comparison test to determine whether the series is convergent or divergent: summation as n=1 to infinity of 3/ n^1/2-1/2
4. use direct comparison test to determine whether the series is convergent or divergent: summation as n=1 to infinity of 5/2+3ⁿ