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.)

re: Analytical solution ======== what if?

Comment 5 of 5 |

(In reply to Analytical solution by Daniel)

Good work, Daniel, but what if you didn´t know "euler´s infinite product", I mean, can you get the equality it proclaims?

Edited on June 8, 2008, 9:44 am

Posted by pcbouhid on 2008-06-08 02:11:44

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