1. ## fourier series

A finite Fourier series is given by the sum
$f(x) = \sum\limits_{n = 1}^N {{a_n}\sin nx = {a_1}\sin x + {a_2}\sin 2x + ... + {a_N}\sin Nx}
$

Show that the mth coefficient am is given by the formula
${a_m} = \frac{1}
{\pi }\int_{ - \pi }^\pi {f(x)\sin mxdx}

$

very confused...

2. Originally Posted by genlovesmusic09
A finite Fourier series is given by the sum
$f(x) = \sum\limits_{n = 1}^N {{a_n}\sin nx = {a_1}\sin x + {a_2}\sin 2x + ... + {a_N}\sin Nx}
$

Show that the mth coefficient am is given by the formula
${a_m} = \frac{1}
{\pi }f(x)\sin mxdx
$

very confused...

The formula is incorrect: you ommited an integral. Check once again and try to prove it by yourself, and if you get stuck somewhere THEN write back.

Tonio

3. okay thanks i've corrected it