Question

Discrete math

Use mathematical induction to prove that n(n+5) is divisible by 2 for any positive integer n.

Answer #1

(10) Use mathematical induction to prove that
7n – 2n is divisible by 5
for all n >= 0.

Prove that 5n2 +15n is divisible by 10 for every n ≥ 2, by
mathematical induction.

Prove by mathematical induction: n3 – 7n + 3 is divisible by
3, for each integer n ≥ 1.

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

(-) Prove that 1·2 + 2·3 +···+ (n−1) n = (n−1)n(n+ 1) /3.
(Discrete Math - Mathematical Induction)

Use Mathematical Induction to prove that for any odd integer n
>= 1, 4 divides 3n+1.

Prove, using mathematical induction, that (1 + 1/ 2)^ n ≥ 1 + n
/2 ,whenever n is a positive integer.

Discrete Math
6. Prove that for all positive integer n, there exists an even
positive integer k such that
n < k + 3 ≤ n + 2
. (You can use that facts without proof that even plus even is
even or/and even plus odd is odd.)

Prove by induction that k ^(2) − 1 is divisible by 8 for every
positive odd integer k.

Use Mathematical Induction to prove that 3n < n! if n is an
integer greater than 6.

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