Re: A86: permanent effects
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Re: A86: permanent effects
Pi does have an end! Look here:
BTW: If you don't understand math very well overlook this and trust me
and my calc2 book.
If you ever get a hold of a calculus book look up Gregory's Series or
Ramanujan's Series in the index. Both show that the series for pi
converges. Ramanujan's converges more quickly than Gregory's though.
Here's the series:
Gregory's:
pi = 4(1 - 1/3 + 1/5 - 1/7 + 1/9 - ...)
derived from the series
x - (x^3)/3 + (x^5)/5 - (x^7)/7 + ...
And of course x grows to infinity
Ramanujan's:
pi = 16(1/5 - (1/3)(1/5)^3 + (1/5)(1/5)^5 - ...) - 4(1/239 -
(1/3)(1/239)^3 + (1/5)(1/239)^5 - ...)
derived from the trigonometric identity
tan a + tan b
tan(a+b) = ---------------
1 - tan a tan b
x goes to infinity here also
Both series are Maclaurin series (that's the switching bakc and forth
between +'s and -'s)
Wyrmlord
egillespie@juno.com
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