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Math 261 Proofs and Fundamentals
Shuyi WENG
Spring 2012
Prof. Bloch
Homework Assignment  May 2, 2012
Exercise 5.3.1
(1) Relation M is an equivalence relation on R.
(2) Relation S is not an equivalence relation on R.
(4) Relation Z is not an equivalence r
Math 261 Proofs and Fundamentals
Shuyi WENG
Spring 2012
Prof. Bloch
Homework Assignment  May 7, 2012
Exercise 6.3.1 (2)
Theorem. The following formula holds for all n N.
12 + 22 + + n2 =
n(n+1)(2n+1)
.
6
Proof. We use proof by induction on N.
For the cas