1. The problem statement, all variables and given/known data I need to use Taylor Expansion to show that: (1+x)^n = 1 + nx + n(n-1)(x^2)/2! + ... 2. Relevant equations y(x0 + dx) = y(x0) + dx(dy/dx) + [(dx)^2/2!](d^2y/dx^2) + ... 3. The attempt at a solution I've only just begun Taylor Expansion, according to my textbook I need the above equation (1+x)^n So: x0 = 1 and dx = x I'm not sure about this next part: y(1+x) = (1+x)^n So: y(x) = x^n dy/dx = nx^n-1 d^2y/dx^2 = (n)(n-1)x^n-2 However putting all of this into the equation I get: y(1+x) = y(1) + (x)(nx^n-1) + [x^2/2!][(n)(n-1)x^n-2] + ... (1+x)^n = 1^n + (nx)(x^n-1) + (n)(n-1)[x^2/2!](x^n-2) + ... (1+x)^n = 1 + (nx)(x^n-1) + (n)(n-1)[x^2/2!](x^n-2) + ... Which I get as my final answer. As you can see, there is a (x^n-1) in the second term, and a (x^n-2) in the third term, that shouldn't be there. So I'm trying to see where I went wrong, please help me out!