Series expansion of sin(x)

[plasmatic]

\(\displaystyle \displaystyle \begin{align} \sin(x)\, &=\, \sum_{i\, =\, 0}^{\infty}\, \dfrac{(-1)^i}{(2i\, +\, 1)!}\, x^{2i+1}

\\ \\ &=\, x\, -\, \dfrac{x^3}{3!}\, +\, \dfrac{x^5}{5!}\, -\, \dfrac{x^7}{7!}\, +\, ...\end{align}\)

 

[Ishuda]

\(\displaystyle \displaystyle \begin{align} \sin(x)\, &=\, \sum_{i\, =\, 0}^{\infty}\, \dfrac{(-1)^i}{(2i\, +\, 1)!}\, x^{2i+1}

\\ \\ &=\, x\, -\, \dfrac{x^3}{3!}\, +\, \dfrac{x^5}{5!}\, -\, \dfrac{x^7}{7!}\, +\, ...\end{align}\)

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

 

[pka]

\(\displaystyle \displaystyle \begin{align} \sin(x)\, &=\, \sum_{i\, =\, 0}^{\infty}\, \dfrac{(-1)^i}{(2i\, +\, 1)!}\, x^{2i+1}

\\ \\ &=\, x\, -\, \dfrac{x^3}{3!}\, +\, \dfrac{x^5}{5!}\, -\, \dfrac{x^7}{7!}\, +\, ...\end{align}\)

What you have posted is correct.

BUT what is your point (question) or otherwise?

BTW: can you see from that why \(\displaystyle \sin(x)\) is an odd function?