I need to find the equations of the following, using Ó (and the n=1 which is at the bottom of the Ó) (and infinity is at the top of the Ó)

1) 5/1 + 8/1 + 1/1 + 14/1 + . . .

2) 6/5 + 9/8 + 14/11 + 21/14 + . . .

3) -6/3 - 4/4 - 2/5 - 0 + . . .

4) 9/1 + 36/4 +27/9 + 144/16 + . . .

5) 20/4 + 25/5 + 30/6 + 35/7 +40/8 + ...

your title says, "geometric series"

none of them are a geometric series

1) I think you have a typo and meant
5/1 + 8/1 + 11/1 + 14/1 + . .
first of all the 1's in the denominator are redundant and you are simply looking at

5 + 8 + 11 + 14 + ... which is (3n+2) with n starting at 1

2) the numerator is generated by n^2 + 5
and the denominator by 3n+2

do you get the idea?

i still need assistance with the rest i don't understand how yu get hose answers..

To find the equations of the given series, we need to identify the patterns in each series and express them in terms of n, where n represents the position of the term in the series.

1) The given series is: 5/1 + 8/1 + 1/1 + 14/1 + ...

We can observe that the numerator increases by 3 in each term, while the denominator remains constant at 1. Therefore, the equation for this series can be written as:

a(n) = (3n + 2) / 1

2) The given series is: 6/5 + 9/8 + 14/11 + 21/14 + ...

In this series, both the numerator and denominator increase by 3 in each term. To represent this pattern, we can write the equation as:

a(n) = (3n + 3) / (3n - 1)

3) The given series is: -6/3 - 4/4 - 2/5 - 0 + ...

In this series, the numerator stays constant at -2, while the denominator decreases by 1 in each term. We can express this as:

a(n) = -2 / (n + 3)

4) The given series is: 9/1 + 36/4 + 27/9 + 144/16 + ...

In this series, the numerator increases by a factor of 3 in each term, while the denominator increases by a factor of 2. The equation for this series is:

a(n) = (3^n * 3) / (2^n)

5) The given series is: 20/4 + 25/5 + 30/6 + 35/7 + 40/8 + ...

In this series, the numerator increases by 5 in each term, while the denominator increases by 1. We can express this pattern as:

a(n) = (5n + 15) / (n + 3)

Note: These equations represent the nth term in each series.