SOLUTION: Let n be a positive integer. Then 2n is always an even number. We say that 2n is the algebraic rendition of an even number. Question: How would we write an odd number algebraica

Question 499288: Let n be a positive integer. Then 2n is always an even number. We say that 2n is the algebraic rendition of an even number. Question: How would we write an odd number algebraically in terms of n?
If n is any positive integer then 2n is always even, for example if n=17, then 2(17)=34, an even number. Since an odd number can be created by simply adding 1 to an even number, the algebraic rendition of an odd number is simply 2n+1 where n is a whole number. For example if n=17, then 2(17) +1 = 35, an odd number. Note that we also use 2n-1 as an odd number.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Yes, either 2n+1 or 2n-1 works.
RELATED QUESTIONS
Use direct proof to prove that the sum of two odd integers say a and b is even. Note... (answered by ikleyn)

Prove algebraically that (2n+1)^2-(2n+1) is an even number for all positive integer... (answered by Fombitz,amalm06,ikleyn,MathTherapy)

1) If n is a real number, then 2n would never be part of which number set? A) a real... (answered by Theo)

If n is any integer, then 2n is an even integer and 2n + 1 is an odd integer.... (answered by Fombitz)

If n is an integer, which of the following represents an odd number? (A) 2n+3 (B) 2n (answered by Alan3354)

prove that the product of any three consecutive numbers is even. So far I have tried , (answered by josgarithmetic,tenkun,amalm06,ikleyn)

Prove that the difference of the squares of two consecutive odd numbers is a multiple of... (answered by richard1234)

prove that if n is a positive integers of 7^2n is an integer positive of... (answered by Alan3354)

Keith and Chi-An are playing a game. Keith chooses a positive integer less than 100.... (answered by rajagopalan)