CJam, 11 10 bytes
1 byte removed thanks to Erik the outgolfer
ri),{W#+}* This uses 1-based indexing.
Explanation
ri e# Read integer, n ) e# Increment by 1: gives n+1 , e# Range: gives [0 1 2 ... n] { }* e# Fold this block over the array W# e# Inverse of a number + e# Add two numbers