Which sum or difference is equivalent to the following expression? 2x+3 over 4A) x/2 + 3/4B) x/2 - 3/4C) 3x/4 + 3/4D) 8x + 24
1 answer:
The correct option is: A)
<em><u>Explanation</u></em>
The given expression is:
If we <u>split the above whole expression into two different fractions</u> with a common denominator, then we will get......
Now, we can <u>reduce the first fraction by dividing both numerator and denominator by 2</u>. So, the simplified expression will be......
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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:
y=
Step-by-step explanation:
Because of the slope, we would assume that it is 1/2 because when you use rise over run, the graph rises 1 unit up and shifts 2 units to the right. The -2 is where the y-intercept is (0, -2) based on the picture seen above. The slope is also positive where it is going up instead of going down.