Question

2 (Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

Answer 1

This series is divergent

F

Explanation:

we are given a series

Firstly, we will find nth term

Numerator:

3, 4, 5,...

so, nth term will be

`a_n=n+3`

Denominator:

4,5,6,....

so, nth term will be

`b_n=n+4`

so, we can find it's nth term as

`c_n=(n+3)/(n+4)`

we can use divergent test

`\lim_(n \to \infty)  c_n=\lim_(n \to \infty) (n+3)/(n+4)`

we can divide top and bottom by n

`\lim_(n \to \infty)  c_n= \lim_(n \to \infty) (n/n+3/n)/(n/n+4/n)`

`\lim_(n \to \infty)  c_n= \lim_(n \to \infty) (1+3/n)/(1+4/n)`

now, we can plug n=inf

`\lim_(n \to \infty)  c_n= (1+0)/(1+0)`

`\lim_(n \to \infty)  c_n=1`

Since, it is non-zero value

so, this series is divergent