MA104 Lab Report 10 - Power Series; Taylor and MacLaurin SeriesName:Student Number:LabWinter 20151. [8marks] Determine the sum of the series2nby completing the following:(a) Use term-by-term differentiation to express1(1-x)2as the sum of an infinite series.∞∑n=1n2
(b) Use your result from (a) to determine a power series respresentation forx(1-x)2.
(c) Differentiate your result from (b) to get a series with coefficients 12,22,32, . . ..
(d) Multiply the result from (c) byxto obtain the desired power series.