Question

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.

Answer 1

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

Explanation:

First term, a = 48

`\text{Common ratio, r = }(1)/(4)`

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

`S_n=(a)/(1-r)\\\\\implies S_n=(48)/(1-(1)/(4))\\\\\implies S_n = 64`

And for sigma notation,

`Sum = \sum_(i=1)^(\infty)a\cdot(r)^i-1\\\\\implies Sum = \sum_(i=1)^(\infty) 48\cdot((1)/(4))^(i-1)`