Prove that:`3^(1/2)xx3^(1/4)xx3^(1/8)xx...=3`

Prove that 9^(1//3)xx9^(1//9)xx9^(1//27)xx...oo=3 .

Prove that 1^(1)xx2^(2)xx3^(3)xx xx n^(n)<=[(2n+1)/3]^(n(n+1)/2),n in N

(4^(-1)xx3^(-1))-:6^(-1)

Prove that 1^1xx2^2xx3^3xx...xn^nlt ((2n+1)/(3))^((n(+1))/(2)

The sum of the series (1)/(3)+(1)/(3^(2)xx2)+(1)/(3^(3)xx3)+(1)/(3^(4)xx4)+... is :

If L=-lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1))) , then the value of L^(4) is _____________.

Simplify: (((-2)/3)^(-2))^(3)xx(1/3)^(-4)xx3^(-1)xx1/6

Simplify 4^(1/3)xx[2^(1/3)xx3^(1/2)]divide9^(1/4)