Limit of product of roots

1. May 4, 2010

bobn

Lt (1 – 1/√2)* (1 – 1/√3)…… (1 – 1/√n+1)
n->∞

There must some simple calculation to find this, but I cannot get this, limit exists since

each tern is less than 1, and limit is more than 0. so limit exists between (1 0).

2. May 4, 2010

tiny-tim

Hi bobn!
Why?

Isn't it less than limn->∞ (1 - 1/2)(1 - 1/3)…(1-1/n) ?

3. May 4, 2010

bobn

haa, I am stupid,

1/√n > 1/n implies, (1- 1/√n) < (1 - 1/n).

4. May 4, 2010