perplexus.info :: Calculus : Evaluate this infinite product

Evaluate this infinite product (Posted on 2008-06-05)

Let:

A₀ = 0
A₁ = √(1/2 + 1/2*A₀)
A₂ = √(1/2 + 1/2*A₁)
A₃ = √(1/2 + 1/2*A₂)
...
A_n = √(1/2 + 1/2*A_n-1)
...

Evaluate, analytically, the infinite product

P = A₁ * A₂ * A₃ * ...

See The Solution Submitted by pcbouhid

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Identity of numeric value

| Comment 2 of 5 |

The numeric value for P in Charlie's post is 2/ð

WHY that should be the product is the question, however, and it's one for which I do not have an answer.

Posted by Paul on 2008-06-06 16:03:28

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