Find the Interval of Convergence of the Series $1+(x-2)+\frac{(x-2)^{2}}{2 !}+\frac{(x-2)^{2}}{3 !}+\frac{(x-2)^{4}}{4 !}$

question 55

Essay

Find the interval of convergence of the series $1+(x-2)+\frac{(x-2)^{2}}{2 !}+\frac{(x-2)^{2}}{3 !}+\frac{(x-2)^{4}}{4 !}$

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Definitions:

1-Hexanamine

An organic chemical compound that is a primary amine consisting of a six-carbon chain ending with an amino group.

Ammonia

A colorless gas with a characteristic pungent smell, consisting of nitrogen and hydrogen (NH3), and is a common nitrogenous waste, particularly among aquatic organisms.

1-Bromohexane

A compound consisting of a six-carbon chain with a bromine atom attached to the first carbon.

Amide Synthesis

The process of forming amide bonds between carboxylic acids and amines, commonly involving methods such as direct coupling or activation of the carboxylic acid.