Homework for Week 1
- Prove that there is no smallest positive rational number.
- Prove that n is odd if and only if n2 is odd.
- Prove that 1+2+22+23+24+...+2n=2n+1-1.
- Prove that for all a except a=1, the fraction (1-an+1)/(1-a) equals the sum 1+a+a2+...+an.
- Prove that if you divide 10n by 9 then the remainder is 1.
Due Friday 1/30