How to calculate Laurent series in mathematica about some point zo and annulus a

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What is the probability of winning a best of 5 series with varying probability in each game?

Suppose two friends, A and B, play a best of 5 (first to 3 wins) of 5 different games. Due to skill levels of each player depending on the game, each game has a different probability for each player to win. The outcome of each game is independent of the outcomes of the others.

Label games as G1, G2, G3, G4, G5 (not necessarily played in order).
P(A wins G(i))=p(i)

What is the probability that player A wins the series?

(for the sake of my question, p(1)=0.35, p(2)=0.7, p(3)=0.55, p(4)=0.5, and p(5)=0.4)

Thanks in advance!

Have you read the Low End Box interview series?

Back in April we started publishing interviews of industry leaders on Low End Box as part of our interview style Q/A sessions. We started talking about this back in March on Low End Talk and we still invite anyone interested in being interviewed as part of this series to speak up!

Thus far we’ve published five in total:

Interview: Q&A with RackNerd CEO Dustin B. Cisneros on Leading, Learning, Help and Execution

Interview: Q&A with Nexus Bytes CEO Nahian on the Hosting Industry and a Customer First Approach

Interview: Q&A with on the Software Industry, Small Business, and Making a Difference

Interview: Q&A with EstNOC CEO Ego Ennok on Web Hosting, Virtualization and Running a Small Business

Interview: Q&A with MXroute Owner Jarland Donnell on Email Delivery, the Hosting Industry and a look back

All four interviews were detailed and informative and if you haven’t read them yet, take a few minutes and do so.

If you have a suggestion for who we should interview next please leave your ideas in the comments below.

Jon Biloh

I’m Jon Biloh and I own LowEndBox and LowEndTalk. I’ve spent my nearly 20 year career in IT building companies and now I’m excited to focus on building and enhancing the community at LowEndBox and LowEndTalk.

sequences and series – How to find the minimum number to be multiplied to k so that it’s last digit is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9?

How to find the minimum number to be multiplied to k so that the last digit of the product is k?

for example if K = 7, then then least number to be multiplied to k to get last digit is 0, 1, 2, 3, 4, 5, 6, 7,

8, 9 are respectively { 10, 3, 6, 9, 2, 5, 8, 1, 4, 7 };

sequences and series – Can anyone explain this, please?

I “discovered” the following when I began fooling around in my head with the numbers on my digital clock. Pretty simple, really: 12:45, for example can be added this way – 1+2+4+5= 12. Now, add the 1+2 and get 3. (Remember the 3 because you’ll see it again.) Now add 12:45 another way. 12+45=57 and 5+7=12 and 1+2=3 – again. Now try 24+15=39 and we’re back to the 12 and 3 again. You can do 124+5=129=12=3 again. No matter how you mix these four numbers up, add them together and then add the sums down to a single digit, you always wind up with 3. This works for huge numbers as well as small ones. If you create a random assortment of numbers – for example, 4739251683902165 and add them together sequentially you get 71. 7+1=8. If you divide them into more than one grouping to add together, each of those groupings will produce a different final number but, when added togrther, those final numbers will equal 8. For example 4739+2165=6904 and 6+9+0+4=19 and 1+9=10 and 1+0=1. Now add the other two groups together – 2,516+8,390=10,906. 1+0+9+0+6=16 and 1+6=7. Add the 1 from the first grouping to the 7 from the second grouping and you’re back to another 8. I’m certain there is a name for this seemingly odd occurrence and a reason it should be. Does anyone know where I might find some information about it? Thank you.

analytic number theory – The Dirichlet series of trigonometric functions

I am searching a question now .In that question i think some ideas. i am really interested in if we can find the dirichlet series of trigonometric functions like sin,cos,tan ,cot or not? if there are ; what kind of trigonometric functions are ?

i think maybe its a research question.So i think my question is appropriate for MO. But if its not, i can delete my question and ask for MSE .Thanks for your answers.