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The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 48 and the common ratio is one fourth. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

Respuesta :

Answer:  

The sum of the given geometric series and its sigma notation is given below :

Step-by-step explanation:

First term, a = 48

[tex]\text{Common ratio, r = }\frac{1}{4}[/tex]

The series is given to be geometric series and the sum of geometric series is given by :

[tex]S_n=\frac{a}{1-r}\\\\\implies S_n=\frac{48}{1-\frac{1}{4}}\\\\\implies S_n = 64[/tex]

And for sigma notation,

[tex]Sum = \sum_{i=1}^{\infty}a\cdot(r)^i-1\\\\\implies Sum = \sum_{i=1}^{\infty} 48\cdot(\frac{1}{4})^{i-1}[/tex]

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