Re: Problem with plotting and simplifying a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg100626] Re: Problem with plotting and simplifying a function*From*: dh <dh at metrohm.com>*Date*: Tue, 9 Jun 2009 06:37:34 -0400 (EDT)*References*: <h0bu5u$8nt$1@smc.vnet.net>

Hi, simply write: Sum[Cos[2 Pi k t], {k, -n, n}] this gives: -1 + 2 Cos[n \[Pi] t] Csc[\[Pi] t] Sin[(1 + n) \[Pi] t] Further, note that the Sin part is zero because Sin is an odd function. Daniel new one wrote: > I have a question that troubles me , and I'll appreciate your advices. > Given Sum of : X_N(t) =Sum [ Exp(j2*Pi*k*t) ] with lower limit -N and upper limit +N , -2<= t <= 2 > I need to calculate x(t) ,so I used Euler : > X_N(t) = Sum e^(j2*pi*k*t) = Sum [ cos(2pi*k*t) + j*sin (2pi*k*t) ]. > > Now ,if I'm mistaken the sinus part becom equal to zero , because the cycle > of sinus is PI . But I have a problem with the Cosinus part , how can I > simplify it ? the "t" parameter interrupts with the simplifying ...... > maybe separating it to conditions ? N=2R ------> even , N=2R+1 --> odd ? > > thanks in advance >