Question

The population of a local species of beetle can be found using an infinite geometric series where a1 = 880 and the common ratio is . Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.

Answer 1

The common ratio is missing

Answer 2

1/4

Answer 3

r = 1/4 = 0.25

Answer 4

since |r| < 1, this means that the infinite series does converge to a finite number

Answer 5

S = a/(1 - r)

S = 880/(1 - 0.25)

S = 1,173.333333...

Round up to get 1,174. That is the upper limit of the population.

You would represent this in sigma notation as