## anonymous 4 years ago single variable calculus . help me friends find the maclaurine series for (i) f(x)=1/1−x

1. klimenkov

$$\frac1{1-x}=1+x+x^2+x^3+..., |x|<1$$

2. anonymous

solution?

3. klimenkov

Yes.

4. anonymous

can you explain how to get it?

5. klimenkov

It is the sum of the geometric sequence.

6. anonymous

oh.. okay2. how to find taylor series then?

7. anonymous

do you know?

8. klimenkov

$$f(x)=f(x_0)+f'(x_0)(x-x_0)+\frac{f''(x-x_0)}{2!}(x-x_0)^2+\ldots+\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n+\ldots$$

9. sirm3d

$\huge f(x)=\sum_{n=0}^{+\infty} \frac{ f^n(a) }{ n! }(x-a)^n$ compute the value of $\huge f^{(n)}(a)$

10. sirm3d

where f^0(a) is the value of the function, f^1(a) is the value of the first derivative. For the maclaurin series, use a = 0.

11. anonymous

@klimenkov : thank you :D @sirm3d : tHANK yOU :D