viete's series for pi

alowje

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a text I have read recently begins the above sequence with a square and halves the sequence from there ; so that the first perimeter ie of the square is4 sqrt 2 and the second term is 1/cos45/2 and so on; the infinite series is then (2pi=4sqrt 2 *1/cos45/2*1/cos45/4 ........) My understanding of viete's series is the form pi = 2*2/sqrt 2*2/sqrt (2 +sqrt 2) and so on ( or a reciprocal form) as an infinite series of nested radicals of 2 My question is that I cannot see how to convert the former series above into the latter I must be missing some algebraic "trick" Can anyone algebraically convert the former to the latter form? Thankyou
ps I understand 1/cos45/2 =2/sqrt (2+sqrt 2) I don't see the algebraic manipulation to get the familiar series.
 
a text I have read recently begins the above sequence with a square and halves the sequence from there ; so that the first perimeter ie of the square is4 sqrt 2 and the second term is 1/cos45/2 and so on; the infinite series is then (2pi=4sqrt 2 *1/cos45/2*1/cos45/4 ........) My understanding of viete's series is the form pi = 2*2/sqrt 2*2/sqrt (2 +sqrt 2) and so on ( or a reciprocal form) as an infinite series of nested radicals of 2 My question is that I cannot see how to convert the former series above into the latter I must be missing some algebraic "trick" Can anyone algebraically convert the former to the latter form? Thankyou
ps I understand 1/cos45/2 =2/sqrt (2+sqrt 2) I don't see the algebraic manipulation to get the familiar series.
You're evidently referring to this: https://en.wikipedia.org/wiki/Viète's_formula

That shows the derivation; are you familiar with the half-angle formula?
 
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