Thursday, September 29, 2005
((a+1)^a) vs. (a^(a+1))
as I fell asleep last night I noticed that only for a=1 and a=2 is ((a+1)^a) > (a^(a+1)).
why is this?
I know, it's pretty arb.
| # | (a^(a+1)) | ((a+1)^a) | who's bigger? |
| 1 | 1 | 2 | ((a+1)^a) |
| 2 | 8 | 9 | ((a+1)^a) |
| 3 | 81 | 64 | (a^(a+1)) |
| 4 | 1024 | 625 | (a^(a+1)) |
| 5 | 15625 | 7776 | (a^(a+1)) |
| 6 | 279936 | 117649 | (a^(a+1)) |
| 7 | 5764801 | 2097152 | (a^(a+1)) |
| 8 | 134217728 | 43046721 | (a^(a+1)) |
| 9 | 3486784401 | 1000000000 | (a^(a+1)) |
| 10 | 1E+11 | 25937424601 | (a^(a+1)) |
| 11 | 3.13843E+12 | 7.43008E+11 | (a^(a+1)) |
| 12 | 1.06993E+14 | 2.32981E+13 | (a^(a+1)) |
| 13 | 3.93738E+15 | 7.93715E+14 | (a^(a+1)) |
| 14 | 1.55568E+17 | 2.91929E+16 | (a^(a+1)) |
| 15 | 6.56841E+18 | 1.15292E+18 | (a^(a+1)) |
| 16 | 2.95148E+20 | 4.86612E+19 | (a^(a+1)) |
| 17 | 1.40631E+22 | 2.18591E+21 | (a^(a+1)) |
| 18 | 7.08235E+23 | 1.04127E+23 | (a^(a+1)) |
| 19 | 3.759E+25 | 5.24288E+24 | (a^(a+1)) |
| 20 | 2.09715E+27 | 2.78218E+26 | (a^(a+1)) |
| 21 | 1.22694E+29 | 1.55194E+28 | (a^(a+1)) |
| 22 | 7.51141E+30 | 9.07846E+29 | (a^(a+1)) |
| 23 | 4.80251E+32 | 5.55723E+31 | (a^(a+1)) |
| 24 | 3.20097E+34 | 3.55271E+33 | (a^(a+1)) |
| 25 | 2.22045E+36 | 2.36774E+35 | (a^(a+1)) |
| 26 | 1.60059E+38 | 1.64232E+37 | (a^(a+1)) |
| 27 | 1.19725E+40 | 1.18377E+39 | (a^(a+1)) |
| 28 | 9.28075E+41 | 8.85409E+40 | (a^(a+1)) |
| 29 | 7.44629E+43 | 6.86304E+42 | (a^(a+1)) |
| 30 | 6.17673E+45 | 5.50619E+44 | (a^(a+1)) |
| 31 | 5.29144E+47 | 4.56719E+46 | (a^(a+1)) |
| 32 | 4.67681E+49 | 3.91243E+48 | (a^(a+1)) |
// posted by werner @ 4:37:00 pm 
