Sequences And Series Of Functions 1

Question 1

A series converges Point wise if

Answer 1

Question 2

Domain of convergence

Answer 2

The of x for which the sequence or series converges

Question 3

f is continuous at x € Δ means

Answer 3

Question 4

The limit of a sequence of continuous functions is continuous is

Answer 4

Question 5

Counter example 2 limits are not interchange

Answer 5

Question 6

Sequence f_n converges to f uniformly on Δ if

Answer 6

Question 7

Compare f_n converges uniformly on Δ with point wise convergence? What is difference?

Answer 7

Question 8

How to prove uniform convergence

Answer 8

Question 9

Prove f_n (x) does not converge to f(x) uniformly on Δ

Answer 9

Question 10

Denote Nth partial sum of series

Answer 10

Question 11

Weierstrass M test

Answer 11

Question 12

Prove Weierstrass M test

Answer 12

Question 13

Prove

Answer 13

Question 14

Radius of convergence of a power series

Answer 14

Question 15

Prove radius of convergence of power series

Answer 15

Question 16

Form of Fourier series

Answer 16

Question 17

Convergence of Fourier series

Answer 17

Question 18

Form of a dirichlet series

Answer 18

Question 19

If the dirichlet series converges for some s=s_0 € R then

Answer 19