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Alexxandr [17]
3 years ago
5

The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 30 and the common rati

o is 2/5. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.
Mathematics
2 answers:
Shkiper50 [21]3 years ago
6 0

Answer:

50 is the answer.

Step-by-step explanation:

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

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

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

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

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

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

Alchen [17]3 years ago
3 0
The sum will be: 

sigma(i = 1 to infinity, 30*(2/5)^i) 

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

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


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