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- To test the series ∞∑k=117√k5∑k=1∞1k57 for convergence, you can use the P-test.(You could also use the Integral Test, as is the case with all series of this type.)Find two power series solutions of (x2+2)y"+5xy'-y=0 about the ordinary point x=0. Include the first three terms of each series.Represent the function 5 ln(4-x) as a power series (Maclaurin series) of: