A researcher finds that 15% of all commuters in a metropolitan area take the train to work. The researcher polls 250 people in t
1 answer:
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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:
Step-by-step explanation:
Volume of cone =
Since we are given that a circular cone has a base of radius r and a height of h that is the same length as the radius
=
=
Surface area of cone including 1 base =
Since r = h
So, area =
=
=
Ratio of volume of cone to its surface area including base :
Rationalizing
Hence the ratio the ratio of the volume of the candle to its surface area(including the base) is