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Arctan Appraisal (Posted on 2014-07-01) Difficulty: 2 of 5
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    
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Some Thoughts 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:

Radian
tm=Time()
t$="0"
for k=0 to 2014
  kb$=Trim$(Str$(k))
  t$=BigAdd$(t$,BigATan$( BigDiv$("1",BigAdd$(BigAdd$(BigMult$(kb$,kb$),kb$), "1"),100) ,100) )
Next
Print BigTan$(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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