Part A: There are 114 red marbles
Part B: There are 114 red marbles because if you multiply the ratio 19:1 times 6 you would get 114:6 (added together gives you 120)
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:
x=-60
Step-by-step explanation:
8/52 or 2/13
Because there is 1 queen and 1 jack in each of the 4 suites. so 2x4=8. Out of 52 cards, then simplify.
Wouldn't it be all the numbers from 1 to 10? This is because in order to convert a fraction to a decimal, you divide the numerator by the denominator. Since the numerator is 0, the decimal would of course be repeating.