
1. 
Juanita and Carlos are in a line that contains n different people, including Juanita and Carlos. If there are exactly k people between Juanita and Carlos, how many different lineups could there be? 

2. 


3. 
Consider the summation . (a) Determine S1, S2, and S3. (b) For what values of n is Sn a perfect square? Explain and justify your response. 