Calculus

posted by .

Prove via Mathematical Induction that

(7*n) - 1 is divisible by 6.

I have that it is divisble when n=1, but not n=2 and so on. How should I write the inductive proofs?

  • Calculus -

    It's obviously not true.

    7*2-1 = 13 which is not divisible by 6

    I think you mean 7^n-1 is divisible by 6

    when n=1, 7^1-1 = 7-1 = 6 is divisible by 6
    assume for n=k
    when n=k+1,
    7^(k+1)-1 = 7*7^k - 1
    = 7*7^k -7 + 6
    = 7(7^k-1) + 6
    but, 7^k-1 is divisible by 6, and 6 is divisible by 6, so 7(7^k-1)+6 is divisible by 6

    since 6a+6b = 6(a+b)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Use mathematical induction to prove that 5^(n) - 1 is divisible by four for all natural numbers n. Hint: if a number is divisible by 4, then it has a factor of 4. also, -1 = -5 +4 This is a take home test so I don't want the answer …
  2. Calculus

    Use mathematical induction to prove that each proposition is valid for all positive integral values of n. 5^n + 3 is divisible by 4.
  3. Discrete Math

    Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. n³ + 5n is divisible by 6 I really do not understand this to much. This is what I have so far: n = 1, 1³ - 5(1) = 6, which is divisible …
  4. Discrete Math

    Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. 5^2n – 2^5n is divisible by 7 If n = 1, then 5^2(1) - 2^5(1) = -7, which is divisible by 7. For the inductive case, assume k ≥ …
  5. Math

    Use mathematical induction to prove that 2^(3n) - 3^n is divisible by 5 for all positive integers. ThankS!
  6. maths

    prove by mathematical induction that 7n+4n+1 is divisible by 6
  7. MATHS

    prove by mathematical induction that 7^n+4^n+1 is divisible by 6
  8. Algebra

    Prove by mathematical induction that 3^(3n+1) + 2^(n+1) is divisible by 5
  9. Mathematical induction. I'm stuck. So far I have..

    For all integers n ≥ 1, prove the following statement using mathematical induction. 1+2^1 +2^2 +...+2^n = 2^(n+1) −1 Here's what I have so far 1. Prove the base step let n=1 2^1=2^(1+1)-1 False. Someone else suggested that …
  10. Algebra ASAP

    so this is a fill in on a worksheet and I am having difficulty as the ones I inserted are incorrect can anybody help me how to do it all, sorry it's a long problem. Show that 3^2n − 1 is divisible by 8 for all natural numbers …

More Similar Questions