contestada

Find the interval of convergence for the series. (Enter your answer using interval notation.)

[infinity]

∑ n! · (4x − 1)^n

n = 1

Respuesta :

LammettHash

By the ratio test, the series diverges since the limit

[tex]\displaystyle \lim_{n\to\infty} \left| \frac{(n+1)! (4x-1)^{n+1}}{n! (4x-1)^n} \right| = \lim_{n\to\infty} |n+1| |4x-1|[/tex]

is not finite.

The series only converges for x = 1/4.

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