Question

the population of a local species of dragonfly can be found using an infinite geometric series where a1=30 and the common ratio is 2/5. write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

Answer 1

The sum of any geometric sequence (if it converges, r^2<1) is of the form:

s(n)=a(1-r^n)/(1-r), a=initial term, r=common ratio, n=number of terms...

s(n)=30(1-0.4^n)/(0.6)

s(n)=50(1-0.4^n)

Since r<1 the sum of the infinite series is just:

s=50