How to write the Taylor Series approximation for arctan?

Here's the Taylor Series approximation:

arctan(x) = x - (1/3)x^3 + (1/5)x^5 - (1/7)x^7...

I want to write a function with two inputs (x as seen in the equation above, n is the number of terms) and two outputs (vec as a row vector where each individual term is stored, and approx as the final approximation).

Here's the beginning of my code. It doesn't work and I'm stuck.

function [vec,approx] = taninv(x,n)
    for i = -1:2:n
        approx = ((-1).^(i+1)).*((x^(2.*i-1))./(2.*i-1));
    end

Answer 1

[Roger Stafford]

You are starting i at -1 which would make the first term

   x^(-3)/(-3)

You had better start i at +1. Also since the i's are all odd as you have set it up, then the exponents of the x terms will all be multiples of 4 plus 1. That isn't the right Taylor series. Better think it out again.

Advice: After writing your code, try manually executing it on paper for a small number of terms to see that the terms are being computed properly.