The period of summation functions

[Luongo]

1. how do i find the period of summation of some function ie: 2^-k or cos(pi k) multiplied by some complex exponential e^i7kt

ie: f( t ) = \sum 2^-ke^i7kt
2. does anyone know the formula for finding the period of summations of complex exponentials? note this is for fourier
3. would i say that omega is 7k by Euler's method. if i converted to sines and cosines, thus the period T = 2pi/7?
is this how i would find the period of this summation?

 

[╔(σ_σ)╝]

The definition of periodicity is as follows:
If T is the period of a function f(t) then,
f(t+ T) = f(t).

Does your answer admit to this definition ?

 

[Luongo]

The definition of periodicity is as follows:
If T is the period of a function f(t) then,
f(t+ T) = f(t).

Does your answer admit to this definition ?

i think so thanks

 

[╔(σ_σ)╝]

You are welcome. :-)

 

[Luongo]

You are welcome. :-)

my friend said i am wrong...?

 

[╔(σ_σ)╝]

my friend said i am wrong...?

What is his reasoning ?