IGNOU MMTE 5 2026 - Find the radius of convergence of the following series.i) &nbsp

Question

Find the radius of convergence of the following series.
i) $\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k!} (z - 1 - i)^k$ $\quad \quad$ ii) $\sum_{k=1}^{\infty}\left(\frac{6k+1}{2k+5}\right)^k(z-2i)^k$

09 Jan 2026

Answer :

Word Count : 194

i) Consider the series (\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k!} (z - 1 - i)^k). The general term is (a_k = \frac{(-1)^{k+1}}{k!} (z - 1 - i)^k). To find the radius of convergence (R), use the formula: [ \frac{1}{R} = \lim_{k \to \infty}

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