Classnotes - MA1020-New
Series and Matrices
Department of Mathematics
Indian Institute of Technology Madras
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Department of Mathematics, IIT Madras
MA-1102
Series & Matrices
Assignment-2
Series Representation of Functions
1. Determine the interval of convergence for each of the following power series:
n+1
X
X
X
xn
xn
n x
(b)
(c)
(1)
(a)
n
n2
n+1
n=1
n=0
n=1
Ans:

Department of Mathematics, IIT Madras
MA-1102
Series & Matrices
Assignment-1
Series
1. Show the following:
ln n
= 0.
n
np
(d) lim n = 0 for x > 1.
n x
(b) lim n1/n = 1.
(a) lim
n
n
(e) lim
n
xn
=0
n!
(c) lim xn = 0 for |x| < 1.
n
x n
= ex
(f) lim 1 +
n
n

Department of Mathematics, IIT Madras
MA-1102
Series & Matrices
Assignment-3
Matrix Operations
1. Show that given any n N there exist matrices A, B Rnn such that AB 6= BA.
1 1 0
2. Let A = 0 1 2 . Compute An .
0 0 1
3. Let A Fmn ; B Fnk ; A1 , . . . , Am

Syllabus
Course Number: MA 1102
Course Title: Series and Matrices
Structure: 3014
Objective: To equip students with series representation of functions of a
real variable, and methods of matrix theory. These topics have
applications in all branches of engi