M7MAD
How to get the right side ?



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M7MAD
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goformit100
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its easy, take inequality in use

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

M7MAD
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I know how to get the left side but I am having a hard time to get the right one :)

lgbasallote
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this is proving yes?

M7MAD
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no , i am trying to solve a fourier series of sawtooth function. and this bn coefficient

lgbasallote
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hmm interesting

lgbasallote
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i believe this is @hartnn 's specialty yes?

M7MAD
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I am new i do not know nobody in here :(

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


hartnn
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what is cos pi ?

M7MAD
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cos pi ? it's 1 ..

hartnn
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and cos 2pi = ?

M7MAD
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one

hartnn
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cos 3pi = ?

M7MAD
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:) .. well what is your point ?

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

hartnn
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cos 1pi = 1
cos 2pi = 1
cos 3pi = 1
cos 4pi = 1

M7MAD
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yeah i see it's 1,1,1 and so on

hartnn
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so cos n*pi= ?

M7MAD
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Under which topic in math can i find such examples ..

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

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

M7MAD
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Awesome

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

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

M7MAD
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Hartnn thank you so much, you saved my life :)

hartnn
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welcome ^_^