Name: Anonymous 2009-01-12 23:56
e^x = \smallint e^x
(1-\smallint)e^x = 0
e^x = (1-\smallint)^{-1} \cdot 0
e^x = (1+\smallint + {\smallint}^2 + {\smallint}^3 + \cdots) \cdot 0
e^x = 1 \cdot 0 + \smallint \cdot 0 + {\smallint}^2 \cdot 0 + {\smallint}^3 \cdot 0 + \cdots
e^x = 0 + 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \cdots
Why the hell does this work?
(1-\smallint)e^x = 0
e^x = (1-\smallint)^{-1} \cdot 0
e^x = (1+\smallint + {\smallint}^2 + {\smallint}^3 + \cdots) \cdot 0
e^x = 1 \cdot 0 + \smallint \cdot 0 + {\smallint}^2 \cdot 0 + {\smallint}^3 \cdot 0 + \cdots
e^x = 0 + 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \cdots
Why the hell does this work?