Here we explore power series of the form [math]\sum_{n=0}^{\infty}c_nx^n[/math]. (If [math]c_n[/math] is not defined at [math]n=0[/math] then the summation might have a different starting point.) We get a sense of what the graph of the power series looks like by examining partial sums [math]y_k=c_0+c_1x+c_2x^2+\cdots+c_kx^k[/math]. For a certain interval of [math]x[/math]-values, the partial sums will converge; check the box by "Show radius of convergence" to see this interval. [br][br]If the polynomial approximation for the power series flows off the screen, you can drag it to see more terms.

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]