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sum Up (Posted on 2014-02-26) Difficulty: 3 of 5
Find the infinite sum of :: 13/31+23/32+33/33+43/34+...

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution probable computer solution | Comment 1 of 5

DEFDBL A-Z
CLS
den = 1
FOR term = 1 TO 45
  num = term * term * term
  den = den * 3
  tot = tot + num / den
  PRINT num; den, tot
NEXT term

shows successive approximations

ind.term                           partial sum          
----------
num denom
1  3                            .3333333333333333         
8  9                            1.222222222222222         
27  27                          2.222222222222222         
64  81                          3.012345679012346         
125  243                        3.526748971193416         
216  729                        3.823045267489712         
343  2187                       3.979881115683585         
512  6561                       4.057918000304832         
729  19683                      4.094955037341869         
1000  59049                     4.111890125150299         
1331  177147                    4.119403659107973         
1728  531441                    4.122655195967192         
2197  1594323                   4.124033210334418         
2744  4782969                   4.124606912568323         
3375  14348907                  4.124842122121218         
4096  43046721                  4.12493727454874         
4913  129140163                 4.124975318483996         
5832  387420489                 4.124990371895381         
6859  1162261467                4.124996273321346         
8000  3486784401                4.124998567698939         
9261  10460353203               4.124999453041893         
10648  31381059609              4.124999792354846         
12167  94143178827              4.124999921594161         
13824  282429536481             4.124999970540883         
15625  847288609443             4.124999988982061         
17576  2541865828329            4.124999995896667         
19683  7625597484987            4.124999998477842         
21952  22876792454961           4.124999999437416         
24389  68630377364883           4.124999999792784         
27000  205891132094649          4.12499999992392         
29791  617673396283947          4.124999999972151         
32768  1853020188851841         4.124999999989835         
35937  5559060566555523         4.124999999996299         
39304  1.667718169966657D+16    4.124999999998655         
42875  5.00315450989997D+16     4.124999999999512         
46656  1.500946352969991D+17    4.124999999999823         
50653  4.502839058909973D+17    4.124999999999936         
54872  1.350851717672992D+18    4.124999999999977         
59319  4.052555153018976D+18    4.124999999999991         
64000  1.215766545905693D+19    4.124999999999996         
68921  3.647299637717079D+19    4.124999999999998         
74088  1.094189891315124D+20    4.124999999999999         
79507  3.282569673945371D+20    4.124999999999999         
85184  9.847709021836113D+20    4.124999999999999         
91125  2.954312706550834D+21    4.124999999999999

The total appears to be 33/8.


  Posted by Charlie on 2014-02-26 12:58:59
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