Taylor series with plus inside

[nhrock3]

i can't understand how the got this variation of taylor series formula
$$f(x+h)=\sum_{k=0}^{\infty}\frac{f^{(k)}(x)}{k!}(h)^k$$

http://mathworld.wolfram.com/TaylorSeries.html

when around some point there is no x-x_0

 

[Mark44]

i can't understand how the got this variation of taylor series formula
$$f(x+h)=\sum_{k=0}^{\infty}\frac{f^{(k)}(x)}{k!}(h)^k$$

http://mathworld.wolfram.com/TaylorSeries.html

when around some point there is no x-x_0

The Taylor series is usually written this way (using y instead of x, though).
$$f(y)=\sum_{k=0}^{\infty}\frac{f^{(k)}(y_0)}{k!}(y - y_0)^k$$

If you let y = x + h, y₀ = x, and y - y₀ = h, you'll get the form you have.