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Nookie1986 [14]
3 years ago
14

The population of a type of local frog can be found using an infinite geometric series where a1 = 84 and the common ratio is one

fifth. Find the sum of this infinite series that will be the upper limit of this population.
Mathematics
2 answers:
aleksley [76]3 years ago
3 0
The series is 84(1+1/5+1/25+...)=84(1/(1-1/5)=84÷4/5=84×5/4=21×5=105. Upper limit is 105.
dedylja [7]3 years ago
3 0

Answer:

The sum is 105

Step-by-step explanation:

Given that the population of a type of local frog can be found using an infinite geometric series where a1 = 84 and the common ratio is one fifth.

we have to find the sum

\text{Common ratio}=r=\frac{1}{5} 

If r^2 infinite series converges, otherwise it diverges.

Since the sum of any geometric sequence is:

S_n=\frac{a(1-r^n)}{(1-r)}

whenever r^2 the sum of the infinite series is

S_n=\frac{a}{(1-r)}

Since a=84 and r=\frac{1}{5} the sum of infinite series

S_n=\frac{84}{(1-\frac{1}{5})}

    =\frac{84}{\frac{4}{5}}

    =\frac{5\times84}{4}=105

Hence, the sum is 105

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<h3>What is an elimination method?</h3>

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

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Find more information about the elimination method here

brainly.com/question/13877817

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also can someone check this too? just want to make sure i got the the first part right before proceed further​
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