decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false. Q) The radius of convergence of the power series representation of a function f(x) depends on the point x0 about which the power series is centered.
decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false.
Q) The radius of convergence of the power series representation of a function f(x) depends on the point x0 about which the power series is centered.
We have given a statement that "The radius of convergence of the power series representation of a function f(x) depends on the point x0 about which the power series is centered."
Power series: A power series is a series in form;
When it is centered at 0(c=0), then the series looks like;
Where an is coefficient of the series, so the convergence of the series depends on the values of x,
Assume there is a number R, for that the power series converges for |x-c|<R and diverges for |x-c|>R,
This number is called the radius of convergence of the series.
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