Find the probability of each event went to 1-6 number cubes are rolled.
1 answer:
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We will have the following:
First, we will have that the population change by:
So, the population changed by 703 people.
It took the follwoing number of years to change from 1431 to 2134:
So, it took 4 years to changes from 1431 to 2134.
The average population growth per year is of 175.75 people per year.
The population in 2000 would have been:
So, the population in 2000 would have been approximately 1429 people.
We will have that the equation for the population would be:
So, the equation would be:
Now, we predict the number of people of the town in 2014:
So, there will be approximately 3890 people of the town in 2014.
Answer:
<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>
Step-by-step explanation:
<u>Convergence of Infinite Series</u>
The series is given as the terms
1 , 9 , 1 , 18 , 27 , 1 , 36 , 1 , 45 ...
For a series to be convergent, the limit of the general term an when n goes to infinity must be 0. In such cases, the sum of all terms tends to a fixed value.
Our series has two clearly different sequences, which define it as a piecewise general term:
If n is odd, then
Otherwise, an is an arithmetic series starting from 9 with a common difference of 9, that is
if n is even.
If we take the limit as n goes to infinity, we don't know which one should be selected, thus we must assume that any of them is a correct option, therefore both of them should converge.
The limit of the function
is 1 when n goes to infinity. Since it's not 0, this piece is not convergent and the entire series isn't either.
But it goes worse because of the limit of the second piece
when n goes to infinity is infinite.
The answer is
<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>