Consider serieswhere |r|

a. Complete the following table showing the smallest value of n, calling it N(r), such that |S - S_n| -4, for various values of r. For example, with r = 0.5 and S = 2, we find that |S - S₁₃| = 1.2 ? 10^-4 and |S - S₁₄| = 6.1 ? 10^-5. Therefore, N(0.5) = 14.

b. Make a graph of N(r) for the values of r in part (a).

c. How does the rate of convergence of the geometric series depend on r?

Transcribed Image Text:

k=0 y = S r N(r) -0.9 -0.7 -0.5 -0.2 0 0.2 0.5 14 0.7 0.9