Math 152 Lab 8
Use Python to solve each problem.
1. Given an=ne –2n
(a) Using the Remainder Estimate for the Integral Test forNterms, plot the upperbound (function) and the line y=.00005 to graphically determine how manyterms are needed to sum ∞n=1 an to within .00005.
(b) Find the sum of the series to within .00005.
(c) Using the Remainder Estimate for the Alternating Series Test forNterms, plot the upper bound (sequence) in the windowy∈[0, .00005]to determine the fewestnumber of terms needed to sum∞n=1(–1)n–1anto within .00005.
(d) Find the sum of the series to within .00005.
2. Given the power series ∞ n=0 (–1)n5 n+1 x n+1 n+ 1:
(a) Simplify an+1 an and find the limit.
(b) State the radius of convergence and the endpoints. Substitute to show whethereach endpoint is in the interval of convergence or not.
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