## DANIEL93 2 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. DANIEL93

solution?

3. klimenkov

Yes.

4. DANIEL93

can you explain how to get it?

5. klimenkov

It is the sum of the geometric sequence.

6. DANIEL93

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

7. DANIEL93

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. DANIEL93

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