What is the Limit of the Product of Roots as n Approaches Infinity?

[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).

 

[tiny-tim]

Hi bobn!

Lt (1 – 1/√2)* (1 – 1/√3)…… (1 – 1/√n+1)
n->∞
…
limit is more than 0 …

Why?

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

 

[bobn]

haa, I am stupid,

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

 

[bobn]

thx for reply tiny-tim