Solve this mathematical question Estaablish the in equality nn≥1 3 5 (2n-1),n∈NUnder what con drf - Maths - Algebra of Matrices

Question

Solve this mathematical question

E s t a a b l i s h   t h e   i n   e q u a l i t y
  n n ≥ 1 3 5 ( 2 n - 1 ) , n ∈ N U n d e r  
w h a t   c o n   d r f   t h e   e q u a l i t
y   h o l d s

Zuhaib Ul Zamann · Accepted Answer

Dear student,
RHS=1*3*5* *2n-1=1×2×3×
×2n-1×2n2×4×6
×2n=2n!2nn!So overall inequality becomes2nn≥2n!n!2nn≥2n2n-1
n+1 Now we know that 2n≥2n2n≥2n-12n≥2n-2⋮          ⋮2n≥n+1So we have 2n2n-n+1+1≥2n2n-1
n+1 ⇒2nn≥2n2n-1
n+1 Hence the given inequality holds for all nRegards

Solve this mathematical question E s t a a b l i s h t h e i n e q u a l i t y n n ≥ 1 . 3 . 5 . . . . . ( 2 n - 1 ) , n ∈ N U n d e r w h a t c o n d r f t h e e q u a l i t y h o l d s

Solve this mathematical question

$E s t a a b l i s h t h e i n e q u a l i t y n^{n} \geq 1.3.5 . . . . . (2 n - 1), n \in N U n d e r w h a t c o n d r f t h e e q u a l i t y h o l d s$