Question: Question # 1. (3 marks) Ryan has been carefully studying power series and has made the following deductions: -=1-1+x -1 +... . Power series can

Question # 1. (3 marks) Ryan has been carefully studying power

Question # 1. (3 marks) Ryan has been carefully studying power series and has made the following deductions: -=1-1+x -1 +... . Power series can be differentiated and if we differentiate we get tag =-1+2x-3x-+4x3+.... Multiplying by -1 we arrive at = 1-21+3x2-4r'+.... Then, if we let x = 1 we conclude 1-2+3 -4+ ... = . Despite the terms in the sequence, 1, -2,3, -4, .. not having a limit of 0, their sum converged to a real value! (a) Which one of the convergence/ divergence tests for series did Ryan just "disprove"? (b) What is the flaw in Ryan's reasoning? Be as detailed as possible when you give your

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