How to solve this sum of combinations?

C_n^2 + 2 C_n^3 + ... + (n-1) C_n^n

Look at the sum closely. N is a constant.

Say we have n=10.

All terms are 0 up to (10-1)C(10,10)=9

Regardless the value of n, this is true throughout.

So, the sum is n-1.

Took me a second before I saw it. You're right; there are exactly zero ways to choose n objects from a set of <n.

There was a "less than n" at the end of that previous comment, but apparently the interpreter thought my less than symbol was some sort of markup or directive. Either way, nice answer as usual, Galactus.