Find the sum of the following series:
1 + 4/7 + 9/49 + 16/343 + .......... to infinity
(In reply to
solution by Charlie)
Adding the terms seems to converge on 1.814814814814814 or 49/27:
DEFDBL A-Z
den = 1
FOR i = 1 TO 40
term = i * i / den
t = t + term
PRINT i * i; den; term; t
den = den * 7
NEXT
1 1 1 1
4 7 .5714285714285714 1.571428571428571
9 49 .1836734693877551 1.755102040816326
16 343 4.664723032069971D-02 1.801749271137026
25 2401 1.041232819658476D-02 1.812161599333611
36 16807 2.14196465758315D-03 1.814303563991194
49 117649 4.164931278633903D-04 1.814720057119057
64 823543 7.771300344972879D-05 1.814797770122507
81 5764801 1.405078857015186D-05 1.814811820911077
100 40353607 2.478093222249005D-06 1.814814299004299
121 282475249 4.283561141316137D-07 1.814814727360414
144 1977326743 7.282559673548095D-08 1.81481480018601
169 13841287201 1.22098470717225D-08 1.814814812395857
196 96889010407 2.022933242652249D-09 1.814814814418791
225 678223072849 3.317492562658571D-10 1.81481481475054
256 4747561509943 5.392241879622821D-11 1.814814814804462
289 33232930569601 8.696193656311357D-12 1.814814814813158
324 232630513987207 1.392766556917884D-12 1.814814814814551
361 1628413597910449 2.216881512554481D-13 1.814814814814773
400 1.139889518537314D+16 3.509112010375117D-14 1.814814814814808
441 7.9792266297612D+16 5.52685141634081D-15 1.814814814814813
484 5.58545864083284D+17 8.665358229701822D-16 1.814814814814814
529 3.909821048582988D+18 1.353003100210231D-16 1.814814814814814
576 2.736874734008091D+19 2.104590293602736D-17 1.814814814814814
625 1.915812313805664D+20 3.262323743803845D-18 1.814814814814814
676 1.341068619663965D+21 5.040756230426055D-19 1.814814814814814
729 9.387480337647754D+21 7.765662070964907D-20 1.814814814814814
784 6.571236236353428D+22 1.193078397733977D-20 1.814814814814814
841 4.5998653654474D+23 1.828314381367119D-21 1.814814814814814
900 3.21990575581318D+24 2.795112864328872D-22 1.814814814814814
961 2.253934029069226D+25 4.263656289873089D-23 1.814814814814814
1024 1.577753820348458D+26 6.490239394722823D-24 1.814814814814814
1089 1.104427674243921D+27 9.860310687574156D-25 1.814814814814814
1156 7.730993719707445D+27 1.495279962591594D-25 1.814814814814814
1225 5.411695603795212D+28 2.263615860324645D-26 1.814814814814814
1296 3.788186922656648D+29 3.421161696770543D-27 1.814814814814814
1369 2.651730845859654D+30 5.162665743914101D-28 1.814814814814814
1444 1.856211592101758D+31 7.779285541283484D-29 1.814814814814814
1521 1.29934811447123D+32 1.17058699132293D-29 1.814814814814814
1600 9.095436801298613D+32 1.759123871622699D-30 1.814814814814814
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Posted by Charlie
on 2006-03-11 12:14:46 |
re: solution --- seems to be wrong
