Fourier Series without complex

[Alex Santos]

Homework Statement

The problem is finding the Fourier series of f(t) = e^(-t) from [0,2] where T=2 and without using complex solution.
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Homework Equations

f(t) = a₀/2 + ∑ (a_nCos(nωt) +b_nsin(nωt)
NOT using f(t) = ∑d_ne^(inωt)

The Attempt at a Solution

I tried once but got completely wrong answer.
it was ∑(4*(-1)ⁿ⁺¹*e^-2+n²π²*e^-2*(-1)ⁿ⁺¹+4+n²π²) / n²π²

When I graphed this up in my texas it showed like a barcode which is definitely wrong.
When I got this solution what I did was extending the function f(t) to be even from [-2,2] and T=4 and went from there so all the b_n would be equal to zero but that was as far as I got. What am I doing wrong here?

Thank you :)

 

[vela]

One thing you're doing wrong is extending the function and changing the period. You're solving a different problem than the one that was given.

As far as your current attempt, you have no sines and cosines in your summation. That's one obvious problem. In any case, you need to show your work. Simply posting an incorrect answer is next to useless. We can't tell where you went wrong if you don't show us what you did.