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.)