Question

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

Answer 1

Answer:

This series is divergent

F

Step-by-step 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

$c_n=\frac{n+3}{n+4}$

we can use divergent test

$\lim_{n \to \infty} c_n=\lim_{n \to \infty} \frac{n+3}{n+4}$

we can divide top and bottom by n

$\lim_{n \to \infty} c_n= \lim_{n \to \infty} \frac{n/n+3/n}{n/n+4/n}$

$\lim_{n \to \infty} c_n= \lim_{n \to \infty} \frac{1+3/n}{1+4/n}$

now, we can plug n=inf

$\lim_{n \to \infty} c_n= \frac{1+0}{1+0}$

$\lim_{n \to \infty} c_n=1$

Since, it is non-zero value

so, this series is divergent