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allsm [11]
3 years ago
5

The population of a local species of beetle can be found using an infinite geometric series a1=960 and the common ratio is .25 w

rite the sum in sigma notation and calculate the sum of possible that will be the upper limit of this population
Sigma 960 (1/4)^i-1 ; the sum is 1280
Signa 960 (1/4)^-1 the sun is divergent
Sigma 960 (1/4)^i sum is 1280
Sigma (1/4)^i sum is divergent

I=1 for them all
Mathematics
2 answers:
inysia [295]3 years ago
7 0
Sigma 960(1/4)^(i-1)

Since r^2<1, the sum is convergent and has a value of

960/(1-1/4)

960/(3/4)

4(960)/3

1280
user100 [1]3 years ago
3 0
<h2>Answer:</h2>

         The answer is:

Sigma 960 (1/4)^i-1 ;    the sum is 1280

<h2>Step-by-step explanation:</h2>

We are given the first term of the geometric sequence as:

a_1=960

Also, the common ratio of the terms in geometric sequence is: \dfrac{1}{4}

We know that if the series is a geometric series than the sum of the terms is given by:

a+ar+ar^2+.....\\\\=a(1+r+r^2+....)\\\\=\sum ar^{n-1}

where a is the first term of the series and r is the common difference.

Here a=960

and r=1/4

Hence,

The sum of the series is:

=\sum 960(\dfrac{1}{4})^{i-1}

Now we know that the sum of the infinite geometric series is given by:

S=\dfrac{a}{1-r}

where S is the sum of the series.

Hence, here the sum of the series is calculated by:

S=\dfrac{960}{1-\dfrac{1}{4}}\\\\\\S=\dfrac{960}{\dfrac{3}{4}}\\\\\\S=\dfrac{960\times 4}{3}\\\\\\S=1280

Hence, the sum is:   1280

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