CMSC 250 Homework 7 Spring 2006

Due Wed March 15 at the beginning of your discussion section.

1. Write the first four terms of the following sequences.
   1. $2$, $1$, $\frac{4}{5}$, $\frac{5}{9}$

   2. $0$, $-8$, $-162$, $-3072$

2. Calculate the sum of the first three terms of each sequence from problem 1 both using a calculator and by hand using exact integer and fractional arithmetic.
   1. $2 + 1 + \frac{4}{5} ~=~ 3\frac{4}{5}$   (by calculator: 3.8)

   2. $0 + -8 + -162 ~=~ -170$

3. Write the product of the first three terms of the sequences from problem 1.
   1. $2 * 1 * \frac{4}{5} ~=~ \frac{8}{5}$

   2. $0 * -8 * -162 ~=~ 0$

4. For each of the following, change the following sums and/or products in expanded form to summation or product notation.
   1. 
      
      $$\sum_{i=1}^{3} \frac{(-1)^i(i+1)}{3^i}2^{4-i}$$
      
      

   2. 
      
      $$\prod_{i=1}^{4} \frac{i^2+1}{x^i}$$
      
      

   3. 
      
      $$\prod_{i=1}^{4} \left( \sum_{j=1}^i \frac{(-1)^{j+1}}{j} \right)^i$$
      
      

Web Accessibility