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

 Infinitely Continued III (Posted on 2010-02-04)
Evaluate:

√(6+2√(7+3√(8+4√(9+5√(10+ ....)))))

 See The Solution Submitted by K Sengupta Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 1 of 7

Based on the following table, as more and more terms are included, the value converges on 4:

To interpret the max coefficient in the table, consider, for max coef = 1, the value is just sqrt(6); for max coef = 2 the value is sqrt(6 + 2*sqrt(7)); for 3, it's sqrt(6 + 2*(sqrt(7 + 3*sqrt(8)))); etc. so for example just the figures shown in the puzzle itself, ignoring the + ... ellipsis, is the value for max coef = 5.

`max coef           value1             2.4494897427831782             3.3602831163652243             3.7242809307825594             3.8777446879222395             3.9447403174010246             3.9746786776817737             3.9882783187782718             3.9945308233068739             3.99743199901716610            3.99878796119930411            3.99942546059193612            3.99972664621995313            3.99986952935495514            3.99993755361378315            3.99997003836743316            3.99998559315208517            3.99999305905319618            3.99999665010796919            3.99999838067682720            3.99999921609209821            3.99999962001047422            3.9999998155807323            3.99999991039593524            3.99999995641878925            3.9999999787827826            3.99999998966129327            3.99999999495795928            3.99999999753914829            3.99999999879806130            3.99999999941254131            3.99999999971268832            3.99999999985939733            3.99999999993115334            3.9999999999662735            3.99999999998346736            3.99999999999189237            3.99999999999602238            3.99999999999804739            3.99999999999904140            3.99999999999952941            3.99999999999976842            3.99999999999988643            3.99999999999994444            3.99999999999997245            3.99999999999998746            3.99999999999999347            3.99999999999999648            3.99999999999999849            3.99999999999999950            451            452            453            454            455            4`

from

DEFDBL A-Z
FOR max = 1 TO 55
v = max * SQR(max + 5)
FOR c = max - 1 TO 1 STEP -1
v = c * SQR(v + c + 5)
NEXT c
PRINT max, v
NEXT

 Posted by Charlie on 2010-02-04 13:48:05
Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (11)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information