Simplifying Fourier Series: Tips and Tricks for Desperate Students

[kring_c14]

fourier series--desperately needing help

Homework Statement

http://www.exampleproblems.com/wiki/index.php/FS1

Homework Equations

in the a$$_{n}$$ on the fifth equal sign, why was (-1 ^n)? how did he arrive at that equation?


have mercy..
its our quiz today
and i really have a hard time on fourier

The Attempt at a Solution

 

[Slaviks]

cos (\pi n) for n = even integer is equal to 1,
while for n = odd inetger, it is equal to -1.
The function (-1)^n has the same property.
Since n is an integer and must be either even or odd,
we can replace cos (\pi n) with (-1)^n .