\(f(x) = \frac{1}{(1-x)}\)
\[ f(x) = \frac{1}{1-x} \] \[ = \sum_{n=0}^{\infty} x^n, x ∈ (−1, 1)\]
\[ f(x) = 1 + x + x^2 + x^3 + x^4 + ....\]
\(f(x) = e^x\)
\[ f(x) = e^x \] \[ = \sum_{n=0}^{\infty} \frac{x^n}{n!}, x ∈ (−1, 1)\] \[ f(x) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24} + ...\]
\(f(x) = ln(1 + x)\)
\[ f(x) = ln(1 + x) \] \[= \sum_{n=0}^{\infty} (-1)^{n+1}\frac{x^n}{n}, x ∈ (−1, 1)\] \[ f(x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + ...\]