The farther a neighbor is, the more it "deviates" from the "real" result. Or in other words, we can trust the closest neighbors more than the farther ones.
To pursue this strategy, we can assign weights to the neighbors in the following way:
The nearest neighbor of an instance gets a weight 1/1 , the second closest gets a weight of 1/2 and then going on up to 1/k for the farthest away neighbor.
This means that we are using the harmonic series as weights: