Evaluate : $\displaystyle\sum_{k=1}^n \left(\frac{{n-1 \choose k-1}}{k}\right)$
Alright so I'm completely stumped, I've never evaluated a summation of $\displaystyle{n \choose k}$.
My best guess is to use the binomial theorem, but I don't know how to change this into a form I could use the theorem on.
A little guidance please?
Best Answer
Hint:
Use the recurrence relation $$\binom nk=\frac nk\binom{n-1}{k-1}$$ and remember that $\displaystyle\sum_{k=0}^n\binom nk=\cdots$