Question

Prove by mathematical indution: If n is a natural number, then 1/2*3 + 1/3*4 + 1/4*5 +....+1/(n +1)(N+2)=n/2n+4

Answer #1

If n is a natural number, then 1 * 5 + 2 * 6 + 3 * 7 + ------ +
n(n +4) = n(n+1)(2n+13)/6.

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

Prove the following using induction:
(a) For all natural numbers n>2, 2n>2n+1
(b) For all positive integersn,
1^3+3^3+5^3+···+(2^n−1)^3=n^2(2n^2−1)
(c) For all positive natural numbers n,5/4·8^n+3^(3n−1) is
divisible by 19

prove that 2^2n-1 is divisible by 3 for all natural numbers n ..
please show in detail trying to learn.

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

Show by induction that 1+3+5+...+(2n-1) = n^2 for all n in the
set of Natural Numbers

Prove the following statement: for any natural number n ∈ N, n 2
+ n + 3 is odd.

How would you prove that for every natural number n, the product
of any n odd numbers is odd, using mathematical induction?

Prove using mathematical induction that
20 + 21 + ... + 2n =
2n+1 - 1 whenever n is a nonnegative
integer.

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

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