Convergence of the Binomial Series
Convergence of the Binomial Series
This Demonstration investigates the convergence (or otherwise) of the binomial series , which, when convergent, converges to the function . The output (in red) is shown in two ways:
1+nx+n(n-1)/2!+…+n(n-1)…(n-r+1)/r!+…
2
x
r
x
n
(1+x)
(a) the partial sum of the series, for a chosen value of between and , as you vary the number of terms ;
x
-2
2
k
(b) the graph (red) of the resulting polynomial function of , as you vary , in the interval .
x
k
[-2,2]
The function is also shown for comparison (blue).
n
(1+x)