The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 48 and the common ratio is one fourth. write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

The sum of the given geometric series and its sigma notation is given below :

Step-by-step explanation:

First term, a = 48

The series is given to be geometric series and the sum of geometric series is given by :

And for sigma notation,

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.

b. x- 48 =120

step-by-step explanation: