Given any infinite series ∑a_k, let N(r) be the number of terms of the series that must be summed to guarantee that the remainder is less than 10^-r in magnitude, where r is a positive integer.

a. Graph the function N(r) for the three alternating p-series for p = 1, 2, and 3. Compare the three graphs and discuss what they mean about the rates of convergence of the three series.

b. Carry out the procedure of part (a) for the series and compare the rates of convergence of all four series.

Transcribed Image Text:

(-1)*+ 00 kP k=1 (-1)*+1 00 k! k=1