The area of a
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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>
Answer:
140 ounces of water and 105 ounces of 35% salt solution.
Explanation:
Let be the ounces of water that need to be added and
be the ounces of 35% solution that need to to be added.
We know that the total of ounces of water and of 35% solution must be 245 ounces:
35% of is the salt, and since no salt is added with addition of
liters of water, this must be equal to the amount of salt in the final 15% solution:
we solve for and get:
We put this value into and solve for
to get:
Thus we have 140 ounces of water and 105 ounces of 35% solution.
Answer:
Some of the possible factorizations of the monomial given are:
Step-by-step explanation:
To factorize the monomia you need to express it as a product of two or more monomials. Therefore, you must apply the proccedure shown below:
- Descompose into prime numbers:
- Then, keeping on mind that, according to the Product of powers property, when you have two powers with equal base you must add the exponents, you can make several factorizations. Below are shown some of the possible factorizations of the monomial given: