Indian Institute of Technology Jodhpur Mathematics 1 (MAL1010) Tutorial 2 2019-20, Semester I 1 Instructor: Dr. Gaurav Bhatnagar Test the following series for the convergence: (a) (b) 1 n 1 n n2 n2 1 n n (c) np n (n 1)q (d) nn x n n n ! (e) (f) (g) n2 1 n n n n en 1 ln n n (h) cos n n (i) (j) (k) (l) 2 1 2 3 22 2 32 3 42 4 2 2 2 1 1 2 2 3 3 1 x 2 1 3 5 x 4 1 3 5 7 9 x6 1 2 4 2 4 6 8 2 4 6 8 10 12 12 12 32 12 32 52 2 12 32 52 7 2 3 x 2 2 2 x 2 2 2 2 x 22 22 42 2 4 6 2 4 6 8 1 1 1 x 1 x 2 x 3 Prove/Disprove (a) Number 0.777 can be represented by a single fraction. (b) Every absolutely convergent series converges. (Hint: The statement is true. Use comparison test to prove the statement. This problem will not be discussed in the Tutorial class.)