A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
prove by induction that ((x^(k))1)=(x1)(x^(k1)+x^(k2)+...+x+1)
i got stuck when i have to prove k=n+1 from k=n being assumed true
 one year ago
prove by induction that ((x^(k))1)=(x1)(x^(k1)+x^(k2)+...+x+1) i got stuck when i have to prove k=n+1 from k=n being assumed true

This Question is Closed

satellite73
 one year ago
Best ResponseYou've already chosen the best response.0something is wrong with that formula

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0what is wrong with the formula?

KingGeorge
 one year ago
Best ResponseYou've already chosen the best response.1Looks correct to me.

KingGeorge
 one year ago
Best ResponseYou've already chosen the best response.1Anyways, you have to start with a base case of k=1. Then, you have\[(x1)\overset{\text{?}}{=} (x1)(1)\]Which is true, so the base case is good.

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0yup i have completed the base case and i got stuck when i assume k=n is true and i want to prove k=n+1 from k=n

KingGeorge
 one year ago
Best ResponseYou've already chosen the best response.1Now you assume true up to some \(n\in\mathbb{Z}^+\). So \[(x^n1)=(x1)(x^{n1}+x^{n2}+...+x+1)\]

KingGeorge
 one year ago
Best ResponseYou've already chosen the best response.1Now, look at \[(x1)(x^n+x^{n1}+x^{n2}+...+x+1).\]This is equal to \[(x1)x^n+(x1)(x^{n1}+x^{n2}+...+x+1)\]which by our inductive hypothesis, is equal to \[(x1)x^n+(x^n1)=x^{n+1}x^n+x^n1=x^{n+1}1.\]

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0ok that makes a lot of sense. thank you so much!

satellite73
 one year ago
Best ResponseYou've already chosen the best response.0oh i read the exponent wrong, sorry
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.