MTH 210 Midterm: MTH 210 Midterm 2006 Winter
Document Summary
031: verify that your paper contains 6 questions on 6 pages, you are allowed an 8 1. 2 11 formula sheet written on both sides: no other aids allowed. Use of scrap paper or additional enclosures is not allowed. If you need more space continue on the back of the page, directing marker where the answer continues with a bold sign. Page 2: prove by induction that n. X i=2 i(i 1) = n(n 1)(n + 1) Page 3: consider the sequence a0 = 1, an = 3an 1 + 2, n > 0. (a) calculate a1, a2, a3, a4. Keep your intermediate answers as you will need them for. Mk the next part of the question. (b) use iteration to nd a formula for the sequence. In particular, your nal answer should not contain sums. Quote any as possible. formulas or rules that you use. Page 4: find a regular expression for the following languages over {0, 1}
