a) Give the definition of sequence of real numbers (Xn). Then give 2 example. b) Give the definition of convergent sequence. Then give 2 example. c) Give the definition of Cauchy sequence. Then give an example 0. d) Show that lim n+1 72
Accepted Solution
A:
Answer:a) Definition of sequence of real numbers: A sequence of real number is the function from set of natural number to the set of real numbers. i.e. f: N → R Example: [tex]S_{n}=\frac{1}{n}[/tex][tex]S_{n}=\frac{n}{n+1}[/tex]b) Definition of convergent sequence: A sequence is said to be convergent if for very large value of n, function will give the finite value.Example: [tex]S_{n}=\frac{1}{n}[/tex][tex]S_{n}=\frac{n}{n+1}[/tex]c) Definition of Cauchy sequence: A sequence is said to be Cauchy Sequence if terms of sequence get arbitrary close to one another.