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The challenge of Ivan and Yana
Jenny asked us to think of some sequences whose growth is different.
Here is what we came up with:
Ivan:
1001, 2001, 3001, ...
1, 2, 4, 8, 16, ...
1, 1024, 59049,...
Is it possible for the terms of the second sequence to surpass the corresponding terms of the first one? What about the corresponding terms of the second and the third?
Check your conjecture with robots and let me know.
Yana: I have two sequences for you:
1, 16, 81, 256, 625,...
1, 8, 27, 64, 125,...
If you start with the second one it will be easier for you to solve the first one, I think.
Comment
Try this instead...
Posted by:
Ken
at
04-02-05
Very nice challenge. It inspired me to train a simple robot (just 6 or 7 small steps) that made the following sequence. I think it grows faster than either Ivan's or Yana's sequences. Can you reason why?
1
4
27
256
3125
46656
823543
16777216
387420489
10000000000
285311670611
8916100448256
302875106592253
11112006825558016
437893890380859375
18446744073709551616
827240261886336764177
39346408075296537575424
1978419655660313589123979
104857600000000000000000000
5842587018385982521381124421
341427877364219557396646723584
20880467999847912034355032910567
1333735776850284124449081472843776
88817841970012523233890533447265625
6156119580207157310796674288400203776
443426488243037769948249630619149892803
33145523113253374862572728253364605812736
2567686153161211134561828214731016126483469
205891132094649000000000000000000000000000000