Probability of a given number of a set of random numbers

[Dragonfall]

Homework Statement

Each week you receive a random number {1,...,n}. You may receive the same number more than once. Each number has 1/n probability of being sent to you. What is the expected amount of time until you receive the number 6?

Homework Equations

I'm not sure what to use here.

The Attempt at a Solution

The probability of receiving any number for the first time at the kth week should be $$(1-1/n)^{k-1}/n$$.

 

[bigplanet401]

Try computing the expectation value of k.

 

[Dragonfall]

I did, I get n, where everyone else seems to get n-1.