Genius guys can u solve this Fourier series problem

[installer2001]

HEllo ,
Plz help me in solving these problems regarding Fourier Series:


1):Find Fourier Sine Series for f(x)=x^2 -Π(pie)<x<Π(pie)
and deduce Π^2/12=1-1/4+1/9-1/16 +-------------------

Π indicates PIE

2):With the help of Fourier Sine series and Fourier Cosine series
f(x)=x+1 0<x<Π(pie)
Deduce 1-1/3+1/5-1/7 --------------------- = Π(pie)/4
and 1+1/(3^2)+1/(5^2)+1/(7^2)--------= Π^2/8

3);Find the Fourier Sine series for function f(x) =e^x 0<x<Π(pie)

 

[HallsofIvy]

Even the genius guys aren't going to do your homework for you. What have you done on this and where do you have a problem?

 

[quasar987]

what the hell does Π mean??!? (kidding)

1: are you sure the problem wants you to develop as a series of sine and not sosines?

 

[installer2001]

i have solved question 3 but please please tell me the hints how to solve question 1 and question 2

 

[HallsofIvy]

The reason quasar987 asked if you are sure that a sine series is wanted rather than cosine is because x² is a even function while sine functions are all odd and any function represented as a sine series between -\pi and \pi will be odd. You should find that the "sine" coefficients are all 0.

 

[installer2001]

Well HallsofIvy my teacher gave me these 3 questions to solve and they did'nt tell anything regarding these questions and also told srudents that these questions are very important from EXAM's POINT Of VIEW. Plz please solve this .

 

[installer2001]

U guys r really genius & gr8. Well i consulted with my class fellow and they told me that tha real question is
1):Find Fourier Series for f(x)=x^2 -Π(pie)<x<Π(pie)
and deduce Π^2/12=1-1/4+1/9-1/16 +-------------------

Π indicates PIE

2):With the help of Fourier SIne series
and Fourier Cosine series
f(x)=x+1 0<x<Π(pie)
Deduce 1-1/3+1/5-1/7 --------------------- = Π(pie)/4
and 1+1/(3^2)+1/(5^2)+1/(7^2)--------= Π^2/8

3);Find the Fourier Sine series for function f(x) =e^x 0<x<Π(pie)