Partial Binomial Expansions, and acceptable notation.

[GeorgeGreen]

What is acceptable summation notation for a binomial expansion of, for example (1+x)^n, from the zeroth to the (n-1)th term?

For example a possible expansion maybe (1+x)^4, where by I would like to write in summation notation that the expansion would be : 1 + 4x + 6(x^2) 4(x^3) . Notice there is no x^4.


My attempts have been largely ambiguous, and I would very much like to hear your thoughts.

With thanks,

John

 

[HallsofIvy]

Such a thing would be
$$\sum_{i=0}^k\begin{pmatrix}n \\ i \end{bmatrix}x^iy^{n-i}$$
for k< n.