benwickersham
contestada

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.

Respuesta :

RickyChen
The sum will be: 

sigma(i = 1 to infinity, 30*(2/5)^i) 

->[tex] \lim_{i \to \infty} \frac{30(1- \frac{2}{5}^{i} )}{ \frac{3}{5} } [/tex]

Which is equal to 30/(3/5) = 50

Answer:

50 is the answer.

Step-by-step explanation:

We have, [tex]a_{1} =30[/tex] and common ratio d=2/5.

So, the general form of the geometric series is [tex]a_{n} =a_{1} *d^{n-1}[/tex], for 'n' is from 1 to infinity.

Hence, the sum in sigma form = [tex]\sum a_{1} *d^{n-1}[/tex], where n goes from 1 to infinity.

Now, the infinite sum of geometric series = [tex]\frac{a_{1} }{1-d}[/tex]

i.e. [tex]\frac{30}{2/5}[/tex] = 50

Hence, the sum which will be the upper limit is 50