anonymous
  • anonymous
prove by induction that ((x^(k))-1)=(x-1)(x^(k-1)+x^(k-2)+...+x+1) i got stuck when i have to prove k=n+1 from k=n being assumed true
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
something is wrong with that formula
anonymous
  • anonymous
what is wrong with the formula?
KingGeorge
  • KingGeorge
Looks correct to me.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

KingGeorge
  • KingGeorge
Anyways, you have to start with a base case of k=1. Then, you have\[(x-1)\overset{\text{?}}{=} (x-1)(1)\]Which is true, so the base case is good.
anonymous
  • anonymous
yup 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
  • KingGeorge
Now you assume true up to some \(n\in\mathbb{Z}^+\). So \[(x^n-1)=(x-1)(x^{n-1}+x^{n-2}+...+x+1)\]
KingGeorge
  • KingGeorge
Now, look at \[(x-1)(x^n+x^{n-1}+x^{n-2}+...+x+1).\]This is equal to \[(x-1)x^n+(x-1)(x^{n-1}+x^{n-2}+...+x+1)\]which by our inductive hypothesis, is equal to \[(x-1)x^n+(x^n-1)=x^{n+1}-x^n+x^n-1=x^{n+1}-1.\]
KingGeorge
  • KingGeorge
That make sense?
anonymous
  • anonymous
ok that makes a lot of sense. thank you so much!
KingGeorge
  • KingGeorge
You're welcome.
anonymous
  • anonymous
oh i read the exponent wrong, sorry

Looking for something else?

Not the answer you are looking for? Search for more explanations.