Fourier coefficients and partial sum of Fejer

[Dassinia]

Homework Statement

f(t) a continuously differentiable function twice over the circle T¹
cr its Fourier coefficients and σn(f,t) partial sum of Fejer.
a.Demonstrate that
http://imageshack.us/a/img94/5992/ds35.png b. Consider k as -n≤k≤n , using cr coefficients calculate
http://imageshack.us/a/img542/8306/7jz2.png

c. Consider a function gn= max | f(t)-σn(f,t) | t in the circle T1
show that lim n*gn=0 n->∞
f is constant

Homework Equations

The Attempt at a Solution

I've calculated
http://img9.imageshack.us/img9/7775/mz30.png
I end up with a +1.. the summation about f(t) is in relative numbers Z using Fourier but here it is |r|>n is it from here that I can "delete" the +1 ?

b.
c.

 

[Dassinia]

a. b. solved !

c. ...