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

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

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 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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