Generating Functions - Differencing

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Here are two examples of how you might use the technique of differencing to find the generating function for a sequence.
  1. Mathematics Exemplified
  2. discrete
  3. math228
  4. sequences
  5. generating-functions
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Комментарии
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How many times we have to roll dice in 10 ways to get sum as 3 ... i hate discrete

__________
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Wonderful! Thanks so much for your teaching!

khoinguyenquang
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Try using differencing twice. The first differencing gives the sequence 3, 9, 15, 21. Then try to find a generating function for THAT sequence. Use differencing on the new sequence to get 6, 6, 6, 6, ... and use the known generating function for that part.

oscarlevin
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How u took that 1-2x+3x²-4x³+5x⁴... As 1/(1+x)².????

sharathg
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In the second example instead of subtracting xA can we add it make

siddharthkatyal
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6:23 In generating function we dont care about convergence too much so it is easier to observe that we have derivative of geometric series here

holyshit
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The generating function for 6x^2+ 6x^3 + ... is 6x^2(1/1-x). The other terms come along for the ride.

oscarlevin