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 Arctan Appraisal (Posted on 2014-07-01)
Determine N, given that:

2014
Σ Arctan (k2+k+1)-1 = Arctan (N)
k=0

*** All angles are in radians.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer timing Comment 2 of 2 |
On my old XP machine UBASIC found the numeric answer in about 1/9 second:

list
10   point 21
20   Tm=time1000
30   for K=0 to 2014
40     T=T+atan(1/(K*K+K+1))
50   next
60   print tan(T),(time1000-Tm)/1000
OK
run
Words for fractionals 21 (Decimals for display 101)
2014.99999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999129055065      0.11

Mintoris Basic on my cellphone took over 19 seconds:

tm=Time()
t\$="0"
for k=0 to 2014
kb\$=Trim\$(Str\$(k))
Next
Print BigTan\$(t\$,100)
SetClipboard BigTan\$(t\$,100)
tm=Time()-tm
print tm/1000

2014.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999965765639

Added on my Windows 7 computer:

Using UBASIC under DOSBox takes 1.3 seconds.

Edited on July 1, 2014, 1:11 pm
 Posted by Charlie on 2014-07-01 13:06:54

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