2. [6 marks] (Induction) Prove that 21 divides 4n+1 + 5 2n−1 whenever n is a...

2. [6 marks] (Induction) Prove that 21 divides 4n+1 + 5 2n−1 whenever n is a positive integer. HINT: 25 ≡ 4(mod 21)

Expert Solution

Colby Messinger answered 1 year ago

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for...

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for all integers n Show all work

5. Without using the method of mathematical induction, prove that 5^n − 3^n + 2n is...

5. Without using the method of mathematical induction, prove that 5^n − 3^n + 2n is divisible by 4 for all natural n.

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2)...

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2) Prove that a finite set with n elements has 2n subsets (3) Prove that every amount of postage of 12 cents or more can be formed using just 4-cent and 5-cent stamps

Use a direct proof to prove that 6 divides (n^3)-n whenever n is a non-negative integer.

By induction: 1. Prove that Σni=1(2i − 1) = n2 2. Prove thatΣni=1 i2 = n(n+1)(2n+1)...

By induction: 1. Prove that Σni=1(2i − 1) = n2 2. Prove thatΣni=1 i2 = n(n+1)(2n+1) / 6 .

(1)Prove 6^(2n)-4^(2n) must be a mutiple of 20 (2)Prove 6^(2n)+4^(2n)-2 must be a multiple of 50

1. Prove or Disprove: If n is a nonnegative integer, then 5 | (24n + 39n)

1. Prove or Disprove: If n is a nonnegative integer, then 5 | (2*4n + 3*9n)

Use a mathematical induction for Prove a^(2n-1) + b^(2n-1) is divisible by a + b, for...

Use a mathematical induction for Prove a^(2n-1) + b^(2n-1) is divisible by a + b, for n is a positive integer

Show by induction that for all n natural numbers 0+1+4+9+16+...+ n^2 = n(n+1)(2n+1)/6.

prove or disprove .if n is a non negative integer, then 5 divides 2 ⋅ 4^n...

prove or disprove .if n is a non negative integer, then 5 divides 2 ⋅ 4^n + 3⋅9^n.

Question