How does one solve this stuff?

>>8596145
https://en.wikipedia.org/wiki/Binomial_coefficient

I mean I could type it into Mathematica with open bounds and know a closed form representation at once.

If you think of binomial coefficents, the first thing the comes to mnd is
(a+b)^k
you could look what that is.

If the coefficient, there are rules to make them smaller (like how to transform one to a sum of two smaller ones)

Pretty sure that suffices

>>8596145

Huh, TIL you can put in negative number in binomial coefficients. You learn something new everyday.

File: 14842126091791180888298.jpg (3MB, 4160x3120px) Image search: [Google]

3MB, 4160x3120px

>>8596151
Am I on the right track here ?

>>8596145
The first term includes the factorial (-1)!

Are you sure this is right? What's the context?

>>8596159
Just for future understanding, you'd also need to change the upper bound of the summation, which would give you 21 choose 20 at the end.

>>8596164
Yes

Are you aware of the formula [math](ax+by)^n = \sum_{k=0}^{n}{n \choose k}(ax)^{n-k}(by)^k?[/math]

>>8596159
You didn't really respond to anything I said in particular, did you?

Write down the formula for (a+b)^k and do pattern matching

>>8596156
https://en.wikipedia.org/wiki/Gamma_function