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: Identity of numeric value ------ a first hint

| Comment 3 of 5 |

(In reply to Identity of numeric value by Paul)

Since you identified the value found by Charlie, that at first sight means nothing, but it is indeed 2/pi, there goes a first hint:

A(1) = sqrt(1/2) = cos(pi/4)

Edited on June 6, 2008, 8:04 pm

Edited on June 6, 2008, 8:04 pm

Posted by pcbouhid on 2008-06-06 20:03:37

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