Question

the population of a local species of dragonfly can be found using an infinite geometric series where a1 = 42 and the common ratio is 3/4. write the sum in sigma notation and calculate the sum that will be the upper limit of this population

Answer 1

@iGreen

Answer 2

\[A. \sum_{i=1}^{\infty}(3/4)42^{i-1},\] the sum is divergent
\[B. \sum_{i=1}^{\infty}(3/4)42^{i-1}\] the sum is 168
\[C. \sum_{i=1}^{\infty}42(3/4)^{i-1}\] the sum is divergent
\[D. \sum_{i=1}^{\infty}42(3/4)^{i-1}\] the sum is 168

Answer 3

@amorfide

Answer 4

you know the term a which is 42
you know the ratio r wh ich is 3/4

you know the geometric series to infinity is sum from 1 to infinite
and the equation is

\[\sum_{1}^{\infty} ar^{k}=\frac{ a }{ 1-r}\]

Answer 5

I probably should have put k=1 on the bottom of that sigma

Answer 6

i understand how you got the equation, i just dont know how to solve it :(

Answer 7

well you would substitute your values

a is the first term
r is the ratio

Answer 8

ok

Answer 9

@phi

Answer 10

@mathstudent55

Answer 11

@thomaster

Answer 12

the answer was D.
gee, thanks for the help guys
(he said sarcastically)