Respuesta :

Answer:

This series is convergent

(A)

Step-by-step explanation:

We are given a series

Firstly, we will find nth term

So, numerator is

[tex]=2n+1[/tex]

So, denominator is

[tex]=n![/tex]

so, nth term will be

[tex]a_n=\frac{2n+1}{n!}[/tex]

now, we can use ratio test

[tex]L= \lim_{n \to \infty} \frac{a_n_+_1}{a_n}[/tex]

[tex]L= \lim_{n \to \infty} \frac{\frac{2n+3}{(n+1)!}}{\frac{2n+1}{n!}}[/tex]

[tex]L= \lim_{n \to \infty} \frac{2n+3}{\left(n+1\right)\left(2n+1\right)}[/tex]

Since, denominator has two n terms

so, we get

[tex]L=0<1[/tex]

So, this series is convergent

Otras preguntas