Ask a New Question

Question

by taking three different values on n, show that a cube of an even natural number n, is always even end cube of an odd natural number n, is always odd.
10 years ago

Answers

Steve
n even:
n = 2k
n^3 = (2k)^3 = 8k^3
an even multiple of a number is always even

n odd:
n = (2k+1)
n^3 = 8k^3 + 4k^2 + 2k + 1
= 2(4k^3 + 2k^2 + k) + 1
The extra +1 at the end makes the result odd.
10 years ago

Related Questions

HELP PLEASE! I am taking my college placement test tomorrow and am working on the sample test now. I... Hi, I am currently taking AP US History and we I have never been a history buff so I am illiterate w... thank you so much for taking so much time into helping me have a perfect french essay! I have done... 1. He was taking down what she said. 2. He was noting down what she said. 3. He was writing down w... 1. We had a lot of fun, taking pictures with Mina's camera. 2. We had a lot of fun, while we wer... how much do you get for taking care of 10 dogs at a doggy daycare with taking care of the other thin... how much do you get for taking care of 10 dogs at a doggy daycare with taking care of the other thin... Taking Your Pet to the Vet (1) Taking your pet to the vet for his or her yearly exam requi... Taking Your Pet to the Vet (1) Taking your pet to the vet for his or her yearly exam requi... You are considering taking out one of two loans. Loan R has a principal of $17,550, an interest rate...
Ask a New Question
Archives Contact Us Privacy Policy Terms of Use