Hello, Check out this free website www.mathebook.net it has several Math e-workbook in Virtual as well as PDF format, the virtual one you can solve online and...
... (2n,n) ; ... Here is such an argument. Take a set of A of 2n objects, and arbitraily divide into two sets B and C such that each of B and C contain n...
... the ... is C ... B ... Good but I wonder if this argument can be generalized to obtain the follow similar Identity! Sum (a = k to n) C(n,a) * C(n,a-k) =...
... B ... Regarding my last post, first I rewrite my identity using Slim's variables. C(2n,n+a) = Sum(k = a to n)(C(n,k)*C(n,k-a)) As one can see except for...
Not about this problem per se, but just as a philosophical point: Yes it's useful to define C(n,k) for all integers k with the understanding that C(n,k) = 0...
A lot more goodies on this at http://www.research.att.com/~njas/sequences/A001791 It is possible this formula could be another also for that sequence. I...
Challenge to find a identity for the product abc, wherein each term contains a triangular variable as a factor and a, b, c are each separately used as the sole...
Hi, sorry for this simple calculus problem, might be OT a little...I have an equation : x' + x = t with x(0) = -1 needs to find the x(t) I got x(t) = t -...
... get ... way ... Where occur a mistake in your calcul ? Correct answeres are: C*exp(-t) for homogenuos eq x'+x=0 x(t)=t-1 a particular solution for...
... get ... way ... tetrakovsky gave a good solution. The separation method only works when the two variables can be completely separated on opposite sides of...
Hello all, In how many ways can 945 be expressed as the sum of consecutive whole numbers? Scroll way down for solution. What property does 945 have that no...
... little...I ... x'+x=t integrating factor =e^t so the answer will be x*i.f.=[t*i.f dt x*e^t=[t*e^tdt x*e^t=(t-1)e^t+c........(1) x=t-1+(c/e^t) x(0)=-1 ...
A.Let n go from 0 to 7 B. Using the 3-bit binary values for 0 to 7, [000,001 ... 110,111] let (a,b,c)*n = (d,e,f) =(a-(4 and n)/4},b-(2 and n)/2,(c-(1 and n)) ...
... n)) ... Yes, writing n as a three digit binary number n = b1b2b3: (a,b,c)*n = (a-b1,b-b2,c-b3) and the sum over all three digit binary numbers can be...
Supposing there's an equation that gives the set of all primes, either recursive or not, what's the application of such a formula? My Uncle use to work for...
Best of Luck to you and your future.... ________________________________ From: bqllpd <no_reply@yahoogroups.com> To: mathforfun@yahoogroups.com Sent:...
Hi, Here is a problem for which I discovered an interesting solution. I want to build a multiplication table so that I can lookup products of numbers up to...
I need to find a recurrence relation for the number of ternary strings of length n that contain none of the strings 101, 202, 102. May you help me please?...
Can anyone help me expand the following expression through x^100 [(x^10-x^130)*(1-x^120)] / [(1-x^20)*(1-x^10)*(1-x^25)] I am trying to figure out the general...
Hi, I plugged it into Pari and got the following. The denominator was reduced to -x^25+1 If you have Mathematica or Maple, you may want to try that. Doing ths...
... strings ... Let a0(n),a1(n),a2(n) be the number of strings (of length n) ending in 0,1,2 respectively, and let T(n) be the total number of such strings: ...
The solution is below. You can close now if you are still challenged. ... wrote: Hi, Here is a problem for which I discovered an interesting solution. I want...
... challenged. ... products ... do ... and ... that ... out ... Not bad. The Intel 8080 processor used widely in the first generation of popular computers...
Here's a link to a prime number formula I figured out in '06 relating to past posts in this group. http://www.angelfire.com/pq/cttn/p_n.pdf BTW, I found a...
... generation ... byte) ... Indeed, we can further reduce memory requirements by using the other gem, (a-b)^2 = a^2+b^2 -2ab and ignore negatives. This way we...
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