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f(0) f'(0)(x-0) f''(0)(x-0)^2
------- + ---------- + -------------
0! 1! 2!

so let's start taking derivative

f'(0)= pi cos(pi x) = pi
f''(0)=-pi^2 sin(pi x)=0
f'''(0)=-pi^3 cos(pi x)=-pi^3

so you see the pattern
pi, 0, -pi^3,0,pi^5,0,-pi^7

right