f(x)=(1+x)^a

N = 3 (slider from 0 to 7, step 1)
a = 0.5 (slider from 0 to 5)
f(x) = If[-1 < x < 1, (1 + x)^(a)]
g = If(N < 1, y = 1, 1 + Sum[(Product[a - k, k, 0, n - 1] / n! * x^(n)), n, 1, N])