All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers > Sequences
Sum to Infinity - 1 (Posted on 2006-03-11) Difficulty: 4 of 5
Find the sum of the following series:

1 + 4/7 + 9/49 + 16/343 + .......... to infinity

No Solution Yet Submitted by Ravi Raja    
Rating: 3.7143 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution --- seems to be wrong | Comment 2 of 12 |
(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

  Posted by Charlie on 2006-03-11 12:14:46
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information