To test this series for convergence ∝
∑ (4^n+7)/7^n
n=1
You could use the limit comparison test, comparing it to the series
∝
∑ r^n
n=1

Where r=???
Completing the test, it shows the series:

r should be 4/7. You're comparing the given series to a geometric series that converges. By the limit comparison test, you have

and since this limit is positive and finite, and the series you're comparing to is convergent, then the first series must also be convergent.

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.

i can't see the picture : /