What is the power series for sqrt(x+1) using the square root algorithm?

[lilcoley23@ho]

How would you go about finding the power series for sqrt(x+1) by applying the square root algorithm. I can do it using binomial expansion and other formulas but I'm not familiar with the square root algorithm involving variables.

 

[HallsofIvy]

Which square root algorithm do you mean? There are several.

 

[Muppetmaster]

How would you go about finding the power series for sqrt(x+1) by applying the square root algorithm. I can do it using binomial expansion and other formulas but I'm not familiar with the square root algorithm involving variables.

$$\int\sqrt{x+1}\rightarrow \frac{2}{3}(x+1)^{\frac{1}{2}}$$

It's just the usual 1/n+1x^n+1.

and nx^n-1

$\frac{d}{dx} \sqrt {x+1} \rightarrow \frac{1}{2(x+1)^\frac{1}{2}}$

Which you can expand to a series using the inequality:

$(2x + r) r\leq a - x^2$