Answer:
D. 8
Step-by-step explanation:
32^(3/5) is the same as ^3.
= 2 because 2^5=32
2^3 = 8
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The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by
Then you want to know the value of
if it exists.
To show the limit exists and that converges to some limit, we can try showing that the sequence is bounded and monotonic.
Boundedness: It's true that . Suppose
. Then
. So by induction,
is bounded above by 7 for all
.
Monontonicity: We have and
. It should be quite clear that
. Suppose
. Then
. So by induction,
is monotonically increasing.
Then because is bounded above and strictly increasing, the limit exists. Call it
. Now,
Solve for :
We omit because our analysis above showed that
must be positive.
So the value of the infinitely nested radical is 7.
Solving this question will involve basic division knowledge.
<em><u>The different positive integer values of n are; 4,6,8,12,24</u></em>
From knowledge on division, we know that when 27 is divided by N and we have 3 as remainder, we can express it as;
= quotient +
Now let us rearrange to get;
-
= quotient
this gives;
= quotient
Now to get how many positive integers can be n, it means all positive values of the quotient must be positive integers as well.
Factors of 24 are; 1, 2, 3, 4, 6, 8, 12, 24
Thus, the possible positive integers will come from this list.
But we can't make use of 1,2,3 as possible values of n because when we divide with 27, we will get either an exact value or 1 as the remainder.
Thus <em>the possible positive integer values of n are; 4,6,8,12,24</em>
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Read more at; brainly.in/question/20088076
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