Calculus

posted by Vincent

Use mathematical induction to prove that each proposition is valid for all positive integral values of n.

5^n + 3 is divisible by 4.

  1. Damon

    5^0+3 = 4
    5^1 +3 = 8
    5^2+3 = 5*5^1 + 3 = 4*5^1 +5+3 =28
    5^3+3 = 5*5^2 + 3 = 4*25 + 5+3 = 128

    5^(n+1) + 3 = 5 * 5^n + 3
    = 4 *5^n + (5^n+3)
    ah ha
    4*5^n is divisible by 4 and so is (5^n+3)

Respond to this Question

First Name

Your Answer

Similar Questions

  1. Pre-cal

    use mathematical induction to prove that 1^2 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6 for all positive integral values of n. My work: n=1: 1(1+1)(2(1)+1)/6 = 1(2)(3)/6 = 6/6 = 1. 1^2+2^2+3^2...(n-1)^2+n^2= [(n-1)(n-1)+2n(n-1)+1]/6 …
  2. 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 …
  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 - Mathematical Induction

    3. Prove by induction that∑_(r=1)^n▒〖r(r+4)=1/6 n(n+1)(2n+13)〗. 5. It is given that u_1=1 and u_(n+1)=3u_n+2n-2 where n is a positive integer. Prove, by induction, that u_n=3^n/2-n+1/2. 14. The rth term of …
  6. Calculus

    Use mathematical induction to prove that the statement holds for all positive integers. Also, label the basis, hypothesis, and induction step. 1 + 5 + 9 + … + (4n -3)= n(2n-1)
  7. Calculus

    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?
  8. Math

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

    Prove by mathematical induction that 3^(3n+1) + 2^(n+1) is divisible by 5
  10. precalculus

    Can you check my answers? 1.Which of the following shows the best next step to prove the following by mathematical induction?

More Similar Questions