Question

Prove by induction that 3^n ≥ 5n+10 for all n ≥ 3.

I get past the base case but confused on the inductive step.

Answer #1

Prove by induction that 5n + 12n – 1 is divisible by 16 for all
positive integers n.

Use mathematical induction to prove that 3n ≥
n2n for n ≥ 0. (Note: dealing with the base case may
require some thought.
Please explain the inductive step in detail.

Prove by mathematical induction that 5n + 3 is a
multiple of 4, or if it is not, show by induction that the
statement is false.

Use mathematical induction to prove that for each integer n ≥ 4,
5n ≥ 2 2n+1 + 100.

Prove by induction that 7 + 11 + 15 + … + (4n + 3) = ( n ) ( 2n
+ 5 )
Prove by induction that 1 + 5 + 25 + … + 5n-1 = ( 1/4 )( 5n – 1
)
Prove by strong induction that an = 3 an-1 + 5 an-2 is even with
a0 = 2 and a1 = 4.

3. Prove by contrapositive: Let n ∈ N. If n^3−5n−10>0,then n
≥ 3.
4. Prove: Letx∈Z. Then5x−11 is even if and only if x is odd.
4. Prove: Letx∈Z. Then 5x−11 is even if and only if x is
odd.

Consider a sequence defined recursively as X0=
1,X1= 3, and Xn=Xn-1+
3Xn-2 for n ≥ 2. Prove that Xn=O(2.4^n) and
Xn = Ω(2.3^n).
Hint:First, prove by induction that 1/2*(2.3^n) ≤ Xn
≤ 2.8^n for all n ≥ 0
Find claim, base case and inductive step. Please show step and
explain all work and details

Use mathematical induction to prove the solution of problem T(n)
= 9T(n/3) + n, T(n) = _____________________________. is correct
(Only prove the big-O part of the result. Hint: Consider
strengthening your inductive hypothesis if failed in your first
try.)

Use Mathematical Induction to prove that 3 | (n^3 + 2n) for all
integers n = 0, 1, 2, ....

Prove that every integer of the form 5n + 3 for n ∈ Z, n ≥ 1,
cannot be a perfect square

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