8.3.10 Dave is playing blackjack at his local casino. He starts with $1,000 and on each hand he bets 50% of his money. If he win
2 answers:
Answer:
The amount Dave got after 3 wins and 2 loose is $843.75. The order of win and loose doesn't matter.
Step-by-step explanation:
- We are given with a word problem
- We are asked to find the amount he had after 5 hands
- We can do this in two steps
Step 1 : Identifying the percentages
Step 2 : Finding the amount left
Step 1 of 2
We are given with a word problem. He bets 50% of his money. If he wins he get his bet, if he loose he will loose the money too. If he wins he will get the money as 150%.
That is, 1.5
If he loose he will loose money by 50%
That is, 0.50
Step 2 of 2
The amount got after 5 hands with 3 wins and 2 loose is,
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Answer:
This series diverges.
Step-by-step explanation:
In order for the series to converge, i.e. it must hold that for any small
>0, there must exist
so that starting from that term of the series all of the following terms satisfy that
.
It is obvious that this cannot hold in our case because we have three sub-series of this observed series. One of them is a constant series with , the other is constant with
, and the third one has terms that are approaching infinity.
Really, we can write this series like this:
If we denote the first series as , we will have that
.
The second series is denoted as and we have that
.
The third sub-series is a constant series and it holds that
.
Since those limits of sub-series are different, we can never find such so that every next term of the entire series is close to one number.
To make an example, if we observe the first sub-series if follows that A must be equal to 1. But if we chose , all those terms associated with the third sub-series will be out of this interval
.
Therefore, the observed series diverges.