Prove-disprove-prove-for-an-interval-as-the-case-may-be-x-1-x-lt-x-1-1-x-1-x-N-x-0-Generalization-of-Q-1700-

Question Number 1729 by Rasheed Ahmad last updated on 04/Sep/15

P r o v e / d i s p r o v e / p r o v e f o r a n

i n t e r v a l a s t h e c a s e m a y b e :

{(x!)}^{\frac{1}{x}} \overset{?}{<} {(x + 1)!}^{\frac{1}{x + 1}}, x \in N [x \neq 0]

(G e n e r a l i z a t i o n o f Q 1700)

Commented by 123456 last updated on 04/Sep/15

x \in N^{*} (x \neq 0)

Commented by 123456 last updated on 04/Sep/15

f (x) = {(x!)}^{\frac{1}{x}}

\lim_{x \to 0^{+}} f (x) = ?

Commented by Rasheed Ahmad last updated on 04/Sep/15

T h a n k s! Q u e s t i o n i s c o r r e c t e d .