Question

Problem for 1 hour

Answer 1

Let \[n \ge 3\] be an integer, and let \[a_1,a_2,a_3,....a_n\] be real numbers such that \[a_1a_2a_3....a_n=1\]
Prove that
\[\huge \color{green}{(1+a_2)^2(1+a_3)^3...(1+a_n)^n>n^n}\]

Answer 2

Well that statement is surely false

Answer 3

and why is it false,it is false for n=1,2

Answer 4

when a_1=(100000)^2 and a_2 =a_3 = 1/100000
(1+1/100000)^2 *(1+1/100000)^3 <3^3

Answer 5

so, it is FALSE