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

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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) About Me  (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.