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Math / Discrete Mathematics and Its Applications 7 / Chapter 2.4 / Problem 43E

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

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What are the values of the following products? Recall that

Chapter 1, Problem 43E

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QUESTION:

What are the values of the following products?

a) $\prod_{i=0}^{10} i$

b) $\prod_{i=5}^{8} i$

c) $\prod_{i=1}^{100}(-1)^{i}$

d) $\prod_{i=1}^{10} 2$

Equation Transcription:

$\prod\limits_{i=0}^{10}i$

${\prod\limits_{i=5}^{8}i}_{\ }^{\ }$

${\prod\limits_{i=1}^{100}i}_{\ }^{\ }(-1{)}^{i}$

$\prod\limits_{i=1}^{10}2$

Text Transcription:

prod_i=0^10 i

prod_i=5^8 i

prod_i=1^100 (-1)^i

prod_i=1^10 2

Questions & Answers

QUESTION:

What are the values of the following products?

a) $\prod_{i=0}^{10} i$

b) $\prod_{i=5}^{8} i$

c) $\prod_{i=1}^{100}(-1)^{i}$

d) $\prod_{i=1}^{10} 2$

Equation Transcription:

$\prod\limits_{i=0}^{10}i$

${\prod\limits_{i=5}^{8}i}_{\ }^{\ }$

${\prod\limits_{i=1}^{100}i}_{\ }^{\ }(-1{)}^{i}$

$\prod\limits_{i=1}^{10}2$

Text Transcription:

prod_i=0^10 i

prod_i=5^8 i

prod_i=1^100 (-1)^i

prod_i=1^10 2

ANSWER:

Solution:

Step 1:

In this problem we need to find the values of the given products.

Note: $\prod\limits_{i=\ 1}^{n}i\ =1\times{}2\times{}3.......\times{}n$ , where $\prod\limits_{\ }^{\ }\$ represents product ..

Given : $\prod\limits_{i\ =\ 0}^{10}(i)$

$\prod\limits_{i\ =\ 0}^{10}(i)=0\times{}1\times{}2\times{}3\times{}4\times{}5\times{}6\times{}7\times{}8\times{}9\times{}10\$ , since from the note.

= 0 , since $0\times{}a=\ 0$ .

Therefore , $\prod\limits_{i\ =\ 0}^{10}(i)=\ 0$ .

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What are the values of the following products? Recall that

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Solution Found!

What are the values of the following products? Recall that

Questions & Answers

Study Tools You Might Need

Chapter: 7 Problem: 23E

Chapter: 21 Problem: 5

Chapter: 9 Problem: 47P

Chapter: 13 Problem: 13.1

Chapter: Problem: 7

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