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.
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Posted by Charlie
on 2014-02-26 12:58:59 |
probable computer solution
