Homework for Week 1

  1. Prove that there is no smallest positive rational number.
  2. Prove that n is odd if and only if n2 is odd.
  3. Prove that 1+2+22+23+24+...+2n=2n+1-1.
  4. Prove that for all a except a=1, the fraction (1-an+1)/(1-a) equals the sum 1+a+a2+...+an.
  5. Prove that if you divide 10n by 9 then the remainder is 1.

Due Friday 1/29