Prove Propositions 32 and 33 of the Maasei Hoshev: a) 1 + (1 + 2) + (1 + 2 + 3) + ... + (1 + 2 + ... + n) =    1 2 + 32 + ... + n 2 , if n is odd; 2 2 + 42 + ... + n 2 , if n is even.

Frank is lending $1,000 to sarah for two years. frank and sarah agree that frank should earn a real return of 4 percent per year. instructions: a. the cpi (times 100) is 100 at the time that frank makes the loan. it is expected to be 113 in one year and 127.7 in two years. what nominal rate of interest should frank charge sarah?