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## Homework Statement

Find the Fourier series defined in the interval (-π,π) and sketch its sum over several periods.

i) f(x) = 0 (-π < x < 1/2π) f(x) = 1 (1/2π < x < π)

2. Homework Equations

2. Homework Equations

a

_{o}/2 + ∑(a

_{n}cos(nx) + b

_{n}sin(nx))

a

_{0}= 1/π∫f(x)dx

a

_{n}= 1/π ∫f(x)cos(nx) dx

b

_{n}= 1/π ∫f(x) sin(nx)

## The Attempt at a Solution

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I've worked out the a

_{0}by splitting the limits and integrating individually for -π < x < 1/2π and 1/2π < x < π. When I did this i got a

_{0}= ½

for a

_{n}= 1/π ∫(upper limit π, lower limit 1/2π) cos(nx) dx

= 1/π[1/n sin(nx)]

= 1/π ((1/n. sin(πn) - 1/n.sin(πn/2))

= 1/nπ(0- sin(πn/2)

Here is where i get stuck as sin(πn/2) is 0 for even values of n and alternates between 1, -1 for odd values.

Can i leave this written in sin form of the Fourier series as every other example i've changed the value of sin/cos to either 0 or (-1)

^{n}.

Thanks for any help!