How to solve this eqn?

f(t) = A/2 -T/2<t<0
-A/2 0<x<t/2

f(t+T) = f(t)

T is the period of the waveform. Determine the fourier series of the periodic wave for an arbituary period T. Find an and bn.
If A = 200/ I+100 and T = 1/f=1/101

please advise how should i solve this eqn?

I can't tell the difference between the function definition and the conditions so you've made it a bit difficult. It seems as though you've introduced an "x" in the conditions without showing how it affects the functions. All in all a very disconnected and confusing post.

As for the fourier coefficients you write down the standard forms and integrate.

Hi,

The x should be t.

f(t) = A/2 -T/2<t<0
-A/2 0<x<t/2

f(t+T) = f(t)

T is the period of the waveform. Determine the fourier series of the periodic wave for an arbituary period T. Find an and bn.
If A = 200/ I+100 and T = 1/f=1/101

please advise how should i solve this eqn?pls advise

I think you are describing a square wave with the arbitary period T. The wave is defined from -T/2 but since the wave is periodic you can start from anywhere( but point that gives the least mathematical complications is better like starting from 0 to T).
You can easily use the standard integral forms to solve this. Only little thing to remember is that you have to separate the function into two parts -T/2 to 0 and from 0 to T/2 because of the discotinuity.

You can find more info here
https://mathworld.wolfram.com/FourierSeries.html
This Url has the answer to you problem(which is fairly standard one)

Try using LATEX, it makes your equations much easier to read.