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Nookie1986 [14]
4 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]4 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]4 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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