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The population of a local species of beetle can be found using an infinite geometric series where a1 = 880 and the common ratio is one fourth. Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.

Respuesta :

kategrier17
the formula is a(1) ÷ (1 - r) 
so 880  ÷ (1 - 1/4) = 880 ÷ (3/4) =1173 1/3 

Answer: The sum would be 1173.3333....

Step-by-step explanation:

Since we have given that

a₁ = 880

r = [tex]\dfrac{1}{4}[/tex]

We need to find the sum in sigma notation;

[tex]\sum a_n=\dfrac{a_1}{1-r}[/tex]

And we need to calculate the sum that will be the upper limit of this population:

[tex]\sum a_n=\dfrac{880}{1-\dfrac{1}{4}}=\dfrac{880}{\dfrac{3}{4}}=\dfrac{880\times 4}{3}=1173.3[/tex]

Hence, the sum would be 1173.3333....

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