Question

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that
Rn(x) → 0.]
f(x) = sin((π x)/3))
f(x)= sum n=0 to infinity ________?

Answer 1

Please state the definition.

Answer 2

define sin(u), then replace u with pi x/3

Answer 3

is it sum n=0 to infinity ((-1)^n (pi)^(2n+1))/(2n+1)factorial )) x^(2n+1) ???

Answer 4

\[sin(u)=\sum_0\frac{(-1)^n}{(2n+1)!}u^{2n+1}\]so yeah
\[sin(pi~x/3)=\sum_0\frac{(-1)^n}{(2n+1)!}\left(\frac{pi}{3}x\right)^{2n+1}\]

Answer 5

thanks