- #1

sooyong94

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## Homework Statement

Use Maclaurin’s theorem to derive the first five terms of the series expansion for ##(1+x)^{r}##, where -1<x<1. Assuming the series, obtained above, continues with the same pattern, sum the following infinite series

##1 + \frac{1}{6} - \frac{(1)(2)}{(6)(12)} + \frac{(1)(2)(5)}{(6)(12)(18} - \frac{(1)(2)(5)(8}{(6)(12)(18)(24)}+...##

## Homework Equations

Maclaurin series

## The Attempt at a Solution

I have taken the derivative of ##(1+x)^{r}## several times and obtained the power series

##1+rx+\frac{r(r-1)}{2!} x^{2} +\frac{r(r-1)(r-2)}{3!} x^{3} + \frac{r(r-1)(r-2)(r-3}{4!} x^4+...##

Now, the problem is, how do I relate with the infinite series above?