Generate the first 30 terms of the geometric series given: r = 0.8, a = 1, n = 30 a, ar, ar?,., ar"-1 a. Calculate the sum and check analytically using n-1 a + ar + ar? + .+ ar"-1 =) ark = a 1-r k=0 b. Calculate the cumulative sums of the sequence n-1 a, a + ar, a + ar + ar2,.,) ark k=0 c. Plot the cumulative sums, what is this tending towards (i.e. the limit) d. Check this limit analytically using 00 Zart = () Eark. k=0