Question

The population of a local species of flies can be found using an infinite geometric series where a1 = 940 and the common ratio is one fifth. Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.

Answer 1

@campbell_st

Answer 2

you have a question where there is a limitings sum because the common ratio is lies between -1 and 1

so the terms in the sum are

\[a_{1} = 940, ~~a_{2} = 940 \times \frac{1}{5}, ~~a_{3} = 940 \times (\frac{1}{5})^2... \]

so the sum notation is

\[\sum_{n=1}^{\infty} 940\times (\frac{1}{5})^{n -1}\]

the limiting sum is

\[S_{\infty} = \frac{a}{1 - r}\]

from the question

r = 1/5 and a = 940

Answer 3

so I need to now plug in those values into the limiting sum equation?

Answer 4

so the sum would be 1175

Answer 5

so the answer would be A

Answer 6

I haven't done the calculation.... hold on

so 1175 seems correct

Answer 7

Okay great!!

Answer 8

and it is true that n-1 is the same thing as i-1?

Answer 9

same thing

Answer 10

awesome! Thank you for your help!