Calculus I Fall 2001 MA113:13-15, 19-21 Russell Brown

Below are the first few assignments after the third test.

• A handout on mathematical induction is available online at http://www.ms.uky.edu/ rbrown/courses/ma113 This supplements the material in Stewart.

• Homework G. Due Monday, 19 November 2001

1. Compute

∑_{k=1}^{n}(2k − 1) for n = 1, 2, 3, 4, 5.

2. Guess a simple formula which gives the value of the sum

∑_{k=1}^{n}(2k − 1).

(You may want to try a few more values of n in the first part.)

3. Use mathematical induction to prove that the guess you made in the previous problem is correct for all values of n.

4. Use the formula

∑_{k=1}^{n} k = \frac{n(n + 1)}{2}

and Theorem (2) on page 259 of the text to provide another way of computing the sum

∑_{k=1}^{n}(2k − 1).

• Homework 12. Due Tuesday 20 November 2001. Late papers will be accepted for full credit on Wednesday, 21 November. §4.2 #2, 24. §4.3 #18, 24, 34.

November 8, 2001