Guichard-Combinatorics-Graph-Theory · Problem 1.3.12

Fundamentals

Mathematics — Probability · binomial-coefficients

Problem

Use

(x+1)^n = \sum_{i=0}^{n} \binom{n}{i} x^i

to find a simple expression for

\sum_{i=0}^{n} \frac{1}{i+1} \binom{n}{i} x^{i+1}

. Then find a simple expression for

\sum_{i=0}^{n} \frac{1}{i+1} \binom{n}{i}