| $$frac{1}{1-x}$$ |
$$1 + x + x^2 ... x^n$$ |
$$sum_{n=0}{infty}xn$$ |
|
| $$frac{1}{1+x}$$ |
$$1 - x + x^2 - x^3 ... (-1)nxn$$ |
$$sum_{n=0}{infty}(-1)nx^n$$ |
|
| $$e^x$$ |
$$1 + x + frac{x2}{2!}+frac{x3}{3!} ... frac{x^n}{n!}$$ |
$$sum_{n=0}{infty}frac{xn}{n!}$$ |
$$all$$ |
| $$sinx$$ |
$$x - frac{x^3}{3!} +frac{x^5}{5!} ... (-1)nfrac{x{2n+1}}{(2n+1)!}$$ |
$$sum_{n=0}{infty}(-1)nfrac{x^{2n+1}}{(2n+1)!}$$ |
$$all$$ |
| $$cosx$$ |
$$1 - frac{x^2}{2!} + frac{x^4}{4!} ... frac{x^{2n}}{(2n)!}$$ |
$$sum_{n=0}{infty}(-1)nfrac{x^{2n}}{(2n)!}$$ |
$$all$$ |
| $$ln(1+x)$$ |
$$x - frac{x^2}{2} + frac{x^3}{3} ... frac{x^n}{n}$$ |
$$sum_{n=1}{infty}(-1){n+1}frac{x^n}{n}$$ |
$$ [-1,1] $$ |
| $$(tanx)^{-1}$$ |
$$x - frac{x^3}{3} + frac{x^5}{5} ... (-1){n}frac{x{2n+1}}{2n+1}$$ |
$$sum_{n=0}{infty}(-1)nfrac{x^{2n+1}}{2n+1}$$ |
|