Problem 8 Score: /25 a) (25 Points):Prove by induction the following partial sum equation: 1 1...
(4) Guess a formula for the sum (2n 1) (2n +1) 1.3 3.5 Prove your guess using induction
(4) Guess a formula for the sum (2n 1) (2n +1) 1.3 3.5 Prove your guess using induction
Induction proofs. a. Prove by induction: n sum i^3 = [n^2][(n+1)^2]/4 i=1 Note: sum is intended to be the summation symbol, and ^ means what follows is an exponent b. Prove by induction: n^2 - n is even for any n >= 1 10 points 6) Given: T(1) = 2 T(N) = T(N-1) + 3, N>1 What would the value of T(10) be? 7) For the problem above, is there a formula I could use that could directly calculate T(N)?...
Problem 8: (i) Use the Principle of Mathematical Induction to prove that 2n+1(-1)" + 1 1 – 2 + 22 – 23 + ... + (-1)22" = for all positive integers n. (ii) Use the Principle of Mathematical Induction to prove that np > n2 + 3 for all n > 2.
Q (8 points) Use mathematical induction to prove the formula 1 X – 1 1 X x(x – 1) 22 2n for all n = 1, 2, 3, ..., and x + 0,1.
induction question, thanks.
(15 points) Prove by induction that for an odd k > 1, the number 2n+2 divides k2" – 1 for all every positive integer n.
prove each of the following theorems using weak
induction
1 Weak Induction Prove each of the following theorems using weak induction. Theorem 1. an = 10.4" is a closed form for an = 4an-1 with ao = 10. Theorem 2. an = (-3)"-1.15 is a closed form for an = -3an-1 with a1 = 15. Theorem 3. In E NU{0}, D, 21 = 2n+1 -1. Theorem 4. Vn e N, 2" <2n+1 - 2n-1 – 1. Theorem 5. In E...
DISCRETE MATHEMATICS
Problem 3 (10 points) Use mathematical induction to prove the following statement for all n 21. For full credit, mention the base case (1pt), the induction hypothesis (1 pt) and the induction step (8 pts). 12 22 32
Prove by induction that for every positive integer n, the following identity holds: 1+3+5+...+(2n – 1) = np. Stated in words, this identity shows that the sum of the first n odd numbers is n’.
prove by mathematical induction
Prove Ś m2 n(n+1)(2n+1)
Discrete Math Question.
(8 pts) Use mathematical induction to prove 13 + 33 +53 + ... + (2n + 1)3 = (n + 1)?(2n+ 4n +1) for all positive integers n.