Answer to Question #260226 in MathCAD for Emely

Question

Prove that the following statements are true by means of mathematical induction n X

(a) ∀n ≥ 1, i=1 i(i!) = (n + 1)! − 1.

(b) 7n −2n is divisible by 5, ∀n ≥ 0.

(c) n! > n2, ∀n ≥ 4.

Answer 1

a)

$\displaystyle{\sum^n_{i=1} }i(i!)=(n-1)!-1$