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expand,
r(r+1)(r+2)(r+3).......(r+k) ?
Mathematics is the science which draws necessary conclusions
Mathematics consists of proving the most obvious thing in the least obvious way.
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That would be absolutely horrible to expand. You'd get a big long polynomial with huge coefficients and it wouldn't look nice at all. Plus, with the number of multiplied terms varying with k, I'm not sure it can even be done.
However, there is a much nicer notation for writing it down.
r*(r+1)*(r+2)*(r+3)*...*(r+k) is equivalent to (r+k)!/(r-1)!.
Why did the vector cross the road?
It wanted to be normal.
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