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w+1 (a) Rewrite 3 2 n(n – 1) with the change of variable m = n+2. n=0

w+1 (a) Rewrite 3 2 n(n – 1) with the change of variable m = n+2. n=0

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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2. (a) Rewrite \( 3 \sum_{n=0}^{w+1} n(n-1) \) with the change of variable \( m = n + 2 \). \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (b) Write \( 19.46 \) as the ratio of two integers. [Do not reduce.] \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (c) Which of the following graphs are possible? (Circle your answer) i. A graph with vertices with degree 3, 6, 5, 3, 1 and 8. A. possible B. not possible ii. A simple graph with vertices of 3, 3, 3 and 3. A. possible B. not possible iii. A graph with 7 vertices and odd total degree. A. possible B. not possible
Transcribed Image Text:2. (a) Rewrite \( 3 \sum_{n=0}^{w+1} n(n-1) \) with the change of variable \( m = n + 2 \). \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (b) Write \( 19.46 \) as the ratio of two integers. [Do not reduce.] \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (c) Which of the following graphs are possible? (Circle your answer) i. A graph with vertices with degree 3, 6, 5, 3, 1 and 8. A. possible B. not possible ii. A simple graph with vertices of 3, 3, 3 and 3. A. possible B. not possible iii. A graph with 7 vertices and odd total degree. A. possible B. not possible
1. (a) Suppose \( c \) is an integer. If \( c \mod 7 = 5 \), what is \( 5c \mod 7 \)? (b) Write \( \binom{32}{12} \) in factorial form. (c) Write \( 4 + 8 + 12 + \cdots + 4k \) as a summation.
Transcribed Image Text:1. (a) Suppose \( c \) is an integer. If \( c \mod 7 = 5 \), what is \( 5c \mod 7 \)? (b) Write \( \binom{32}{12} \) in factorial form. (c) Write \( 4 + 8 + 12 + \cdots + 4k \) as a summation.
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