fusetton 3)Find expansion. for at power and find the radias of convergence the Series dz atiz

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A: Calculating the limit of the series as k tends to infinity.

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A: Sol :-Given  ∑n=1∞ (-1)n+1n Sin nπ2             an = (-1)n+1n Sin nπ2                   =(-1)n+1×1n×…

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A: In this question, we use the exponential series to expand f(z)= sin(z) as the Maclaurin series.

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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