All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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)
...
An = √(1/2 + 1/2*An-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.)
 For what it's worth (numerical value) | Comment 1 of 5
` i     A(i)              partial P 1 0.7071067811865476 0.7071067811865476 2 0.9238795325112867 0.6532814824381883 3 0.9807852804032304 0.6407288619353766 4 0.9951847266721969 0.6376435773361455 5 0.9987954562051724 0.6368755077217536 6 0.9996988186962042 0.6366836927259824 7 0.9999247018391445 0.6366357516148734 8 0.9999811752826011 0.6366237671267633 9 0.9999952938095762 0.636620771054086910 0.9999988234517019 0.636620022039002111 0.9999997058628822 0.636619834785423712 0.9999999264657179 0.636619787972041213 0.9999999816164293 0.636619776268696414 0.9999999954041073 0.636619773342860215 0.9999999988510269 0.636619772611401216 0.9999999997127567 0.636619772428536417 0.9999999999281892 0.636619772382820218 0.9999999999820472 0.636619772371391119 0.9999999999955118 0.636619772368533820 0.9999999999988780 0.636619772367819521 0.9999999999997196 0.636619772367641022 0.9999999999999298 0.636619772367596423 0.9999999999999825 0.636619772367585224 0.9999999999999956 0.636619772367582425 0.9999999999999989 0.636619772367581726 0.9999999999999998 0.636619772367581627 1.0000000000000000 0.636619772367581628 1.0000000000000000 0.6366197723675816`
`DEFDBL A-Zp = 1a = 0FOR i = 1 TO 40 a = SQR(.5 + .5 * a) p = p * a PRINT USING "## "; i; PRINT USING "#.################ "; a; pNEXT`

 Posted by Charlie on 2008-06-05 12:27:29

 Search: Search body:
Forums (0)