V = {f:[-pi,pi] -> R}

<f,g> = int_{-pi}^pi f(x)·g(x) dx

No R^n
u = (x1,x2,...,xn)
v = (y1,y2,...,yn)

<u,v>  = sum_{i=1}^n u_i·v_i

-----------------------------
a_n = - (n-1)² + n²

a_1 = 1² - 0²
a_2 = 2² - 1²
a_3 = 3² - 2²

a_1 + a_2 + a_3 
= -0² + 1² 
  -1² + 2²
  -2² + 3²
= -0² + 3²

sum _{i=1}^n a_i = -0² + n²

b_n = 1/n² - 1/(n-1)²

sum_{i=1}^3 sen( k pi (i+1) ) - sen( k pi (i) )