integration

just explain 8 & 9, and you can just answer for the rest of them(no explanation).

Determine whether the following series converge or diverge. Choose (C) if the series converges, and (D) if it diverges. In(n3) 1. M n=2 5n 2. n In(n2) n=2 3. n=2 n(In(n))2 00 n - 1 2n 4. 5n + 6 n=1 00 n 5. 5n + n 6. + n=0 00 n2 7 . (1/3)n8. Given that the series an converges to L and an = f(n) where f is a continuous positive decreasing function, n=1 which of the following is true? A . f(x) da diverges B. f(x) dx = L C. f(x) dx converges D. lim an = L n E. None of the above152 9. Consider the series M n= (n + 4)! After applying the ratio test, which of the following is the resulting inequality that shows whether the series converges or diverges? 15 A. lim oo n + 5 15 C. lim 1, diverges n +4 E. lim 15 > 1, diverges F. None of the aboveDetermine whether the following series is absolutely convergent, conditionally convergent or divergent. Choose (A) for absolute convergence, (C) for conditional convergence and (D) for divergence. 10. (-1)" In(n) n2 n=2 (-1)n32n+1 11. 25n-1 n=1 (-1 )n 12. n=1 Vn2+1 (-1)" 13. 73 + 5 n=1 14. (-1)" (n+ 2)2 M n=1 (n + 1)(n +3) (-1)n 50 n2 15. n! n=1 16. (-1)"(n7 + 2n6 - 12) (n9 - 3n1 + 2n) n=1 17. (-1)" arctan(n) n = n2 +1