Find Limit of Sequence An: 1-1/(n(n+1)/2)

[4c0]

Homework Statement

Find limit of sequence An=(1-1/3)(1-1/6)...(1-1/(n(n+1)/2))

Homework Equations

The Attempt at a Solution

I just found limit of 1-1/(n(n+1)/2) when n→∞,which is 1.Is that a proper solution?

 

[Curious3141]

Homework Statement

Find limit of sequence An=(1-1/3)(1-1/6)...(1-1/(n(n+1)/2))

Homework Equations

The Attempt at a Solution

I just found limit of 1-1/(n(n+1)/2) when n→∞,which is 1.Is that a proper solution?

Homework Statement

Homework Equations

The Attempt at a Solution

I believe they're asking you to find the limit of that infinite product, not just the final term (the limit of which is clearly 1, as you've found).

Try to find an expression for the general term in terms of n. It'll be a quotient. Factorise the numerator.

Now see what happens when you multiply one term by the next. Then multiply by the next. Do this until you see a pattern emerging. What terms cancel out and what are you left with?