please show full solution and steps thanks

6. (10pts) Use limit comparison test that determine whether the series converges or n 2 diverges. Zn=2 n4-n-1 7. (10pts) Determine whether the series converges or diverges. En=1(-1)n+1. n+1 In (n+1) xam3 Page 1 of 2 8. (8pts each) Determine whether the series converges. (a) En 2n n=1 n! n 9. (5pts) Show that the following series converge. Ln=1 cos n n6 10. (8pts) Find the nth Maclaurin polynomial for f(x) = e-x , n=3 11. (8pts) Find nth Taylor polynomial centered at c. f(x) =- VX , n=4, c = 2