Answer and step-by-step explanation:
Please look at the picture above for the solutions and answers.
The given fractions are all geometric sequences. They all have common ratios and it is used in finding the sum of each set of fractions.
The formula for to find the sum of a geometric sequence is:
[tex]Sn = \frac{A1(1-r^n)}{1 - r} [/tex]
where
Sn is the sum of the nth terms,
A1 is the first term,
n is the number of terms and
r is the common ratio.
*Terms are also the numbers of a sequence.
In the given sequence of fractions, the only given values are the first term and the last term. We need the common ratio and the number of terms to solve it.
To do this, let's use the formula to find the number of terms which is:
[tex]An = A1(r) {}^{n - 1}
[/tex]
Then to find the common ratio, simply divide each term by the previous term.
