Is the following statement true or false? n+1 For every odd integer n, To answer this question, let n be any odd integer. By definition of odd, n = 2k + 1 for some integer k, and so, by substitution, A- [2k *1| Starting with this equality, express in terms of ke n+1 Also, when is expressed in terms of k and is completely simplified, the result is 2 -k+1 2 Since the expression in k for n+ 1 as the expression in k for , the given statement is true is the same 2 Need Help? Read It
Is the following statement true or false? n+1 For every odd integer n, To answer this question, let n be any odd integer. By definition of odd, n = 2k + 1 for some integer k, and so, by substitution, A- [2k *1| Starting with this equality, express in terms of ke n+1 Also, when is expressed in terms of k and is completely simplified, the result is 2 -k+1 2 Since the expression in k for n+ 1 as the expression in k for , the given statement is true is the same 2 Need Help? Read It
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Is the following statement true or false?
For every odd integer n, 1
To answer this question,
n be any odd integer. By definition of odd,n= 2k + 1 for some integer k, and so, by substitution,
-|K* 1. Starting with this equality, express " in terms of k as simply as possible without using the ceiling notation. The result is
Also, when " is expressed in terms of k and is completely simplified, the result is
2
n+1
k+1
Since the expression in k for
is the same v
as the expression in k for , the given statement is true
Need Heln? Read I](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4add83d5-7785-4594-8930-722908e420ac%2F802d21c4-2510-4a3b-9a65-d7d994d51450%2Foqbwje_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Is the following statement true or false?
For every odd integer n, 1
To answer this question,
n be any odd integer. By definition of odd,n= 2k + 1 for some integer k, and so, by substitution,
-|K* 1. Starting with this equality, express " in terms of k as simply as possible without using the ceiling notation. The result is
Also, when " is expressed in terms of k and is completely simplified, the result is
2
n+1
k+1
Since the expression in k for
is the same v
as the expression in k for , the given statement is true
Need Heln? Read I
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