Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

tux

  • 3 years ago

Prove by induction 7^n+10 < 8^n

  • This Question is Closed
  1. tux
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For n>=2

  2. fwizbang
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    For n=2, 7^2 + 10 =59 < 64 so its true for n=2. Assume 7^n + 10 <8^n for some n>=2. Then 8(7^n+10) <8^(n+1) (7+1)(7^n+10) < 8^(n+1) 7^(n+1)+ 7^n +70 + 10 < 8^(n+1) 7^(n+1) +10 < 8^(n+1) -7^n -70 < 8^(n+1) So if the statement is true for n, its true for n+1, By induction, its true for all n>=2.

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy