By the Stolz-Cesaro theorem, this limit exists if
also exists, and the limits would be equal. The theorem requires that
be strictly monotone and divergent, which is the case since
.
You have
so we're left with computing
This can be done with the help of Stirling's approximation, which says that for large
,
. By this reasoning our limit is
Let's examine this limit in parts. First,
As
, this term approaches 1.
Next,
The term on the right approaches
, cancelling the
. So we're left with
Expand the numerator and denominator, and just examine the first few leading terms and their coefficients.
Divide through the numerator and denominator by
:
So you can see that, by comparison, we have
so this is the value of the limit.
Answer:
9
Step-by-step explanation:
I replaced the missing variable with x and solved the equation from there.
Answer:
Concept: Binomial Multiplication
- (x-1)(x-9)
- x^2-9x-x+9
- x^2-10x+9
Answer:
Its 16
Step-by-step explanation:
i had the same question and this was the answer on the unit test
B(the student was a freshman or received a C)