SOLUTION: The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 30 and the common ratio is two fifths. Write the sum in sigma notation and

Question 883766: The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 30 and the common ratio is two fifths. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.
a)the summation of 30 times two fifths to the i minus 1 power, from i equals 1 to infinity.; the sum is 50.
b)the summation of 30 times two fifths to the i minus 1 power, from i equals 1 to infinity.; the sum is divergent.
c)the summation of two fifths times 30 to the i minus 1 power, from i equals 1 to infinity.; the sum is 50.
d)the summation of two fifths times 30 to the i minus 1 power, from i equals 1 to infinity.; the sum is divergent.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
S = a/(1 - r)

S = 30/(1 - 2/5)

S = 50

So the sum is 50.

The sigma notation is

So the answer is choice a)

a)the summation of 30 times two fifths to the i minus 1 power, from i equals 1 to infinity.; the sum is 50.
b)the summation of 30 times two fifths to the i minus 1 power, from i equals 1 to infinity.; the sum is divergent.
c)the summation of two fifths times 30 to the i minus 1 power, from i equals 1 to infinity.; the sum is 50.
d)the summation of two fifths times 30 to the i minus 1 power, from i equals 1 to infinity.; the sum is divergent.
RELATED QUESTIONS
This is a question on my study guide for my test and I don't know how to solve this. If I (answered by ewatrrr,Theo)

Find the sum of an infinite geometric series where a1 = 180, and the common ratio is r = (answered by math_tutor2020,ikleyn)

What is the sum of the infinite geometric series with a1 = 27 and r =... (answered by longjonsilver)

find the sum of the infinite geometric series a1=27 and r=... (answered by jim_thompson5910)

How would I find the sum of the infinite geometric series, if it exists with a1 = 18 and... (answered by stanbon)

find the sum of infinite geometric series: a1=26,... (answered by benazir.sj@gmail.com)

1.) Find the indicated term using the given information: a20=45, a10=25, a1=? 2.) Find (answered by Fombitz)

If the common ratio of an infinite series is 3 / 2, it is converging and a sum can be... (answered by jim_thompson5910)

What is Sn of the geometric series with a1 = 4, an = 256 and n =... (answered by Earlsdon)