## M7MAD 3 years ago How to get the right side ?

2. goformit100

its easy, take inequality in use

3. lgbasallote

there was once a famous quote..."one must go left to turn right"

I know how to get the left side but I am having a hard time to get the right one :)

5. lgbasallote

this is proving yes?

no , i am trying to solve a fourier series of sawtooth function. and this bn coefficient

7. lgbasallote

hmm interesting

8. lgbasallote

i believe this is @hartnn 's specialty yes?

I am new i do not know nobody in here :(

10. hartnn

speciality ? no. M7, what is cos pi = ?

just have a look to this example in wikibidia http://en.wikipedia.org/wiki/Fourier_series

12. hartnn

what is cos pi ?

cos pi ? it's -1 ..

14. hartnn

and cos 2pi = ?

one

16. hartnn

cos 3pi = ?

:) .. well what is your point ?

18. hartnn

see the pattern .... cos n*pi = ?

19. hartnn

cos 1pi = -1 cos 2pi = 1 cos 3pi = -1 cos 4pi = 1

yeah i see it's 1,-1,1 and so on

21. hartnn

so cos n*pi= ?

Under which topic in math can i find such examples ..

23. hartnn

just use generalization : cos n*pi = \(\huge (-1)^n\)

24. hartnn

when i put 1, i get -1, when i put n=2, i get +1 and so o n

Awesome

26. hartnn

and -cos (n*pi) = (-1)(-1)^n = ?

27. hartnn

and i think sin n*pi will be easier for you to figure out

Hartnn thank you so much, you saved my life :)

29. hartnn

welcome ^_^