# Math Help - Convergence

1. ## Convergence

Use the appropriate test to decide whether the following series converge or not:

a) $\sum \limit_{n=1} ^{\infty} \frac{3n^2 - 2n + 1}{2n^2 + 5}$

b) $\sum \limit_{n=1} ^{\infty} \frac{3n^2 - 2n + 1}{2n^4 + 5}$

c) $\sum \limit_{n=1} ^{\infty} \frac{n^3 4^n}{3(n!)}$

d) $\sum \limit_{n=1} ^{\infty} \frac{2 + 3 sin~n}{5n^2 + 2}$

Could someone please help :-). Thank you

2. a) A series does not converge if the terms do not tend to zero. In this series the terms tend to 3/2.

b) A series converges if the absolute value of each term is less than the corresponding term of a series known to converge. In this case compare with the series 2/n^2.

c) A series converges if the ratio of successive terms tends to a limit k which is strictly less than 1. In this case the ratio of successive terms tends to zero.

d) Use one of the previous criteria: left as an exercise which one ...