Originally Posted by **Nichelle14**

I need a little help on this problem:

1/2 x 3/4 x ... x (2n-1)/2n <= 1/(sqrt(3n+1)

I know that I have to show that for n= 1 works first and it does. Then I know that I need to show for n+1.

This is what I did, I first added n+1 to both sides

this is what I got: 1/2 x 3/4 x ... x (2n-1)/2n x [2(n+1) - 1]/2(n+1)<=

1/(sqrt(3(n+1)+1))

now i know that the first part of what I did on the LHS is <= to the RHS, so I substituted: and got this:

1/(sqrt(3n+1) x (2n+1)/(2n+2) <= 1(sqrt(3n+4))

Am I on the right track here?