Каkов период десятичной ДРоби 1/((10^10)-1)^2 ?
ru_math — 26.09.2021сегодня возился во всякими древними числами и вот набрёл на довольно неожиданное десятичное разложение.
хотел было посмотреть на периодическую дробь и длину её периода опредеделить на глазоk,
а тут такая вылазит последовательность натуральных чисел и нулей и не видно им конца.
Каkов период десятичной ДРоби 1/((10^10)-1)^2 ?
1/((10^10)-1)^2 = 1/99999999980000000001 = 1.00000000020000000003000000000400000000050000000006000000000700000000080000000009000000001000000000110000000012000000001300000000140000000015000000001600000000170000000018000000001900000000200000000021000000002200000000230000000024000000002500000000260000000027000000002800000000290000000030000000003100000000320000000033000000003400000000350000000036000000003700000000380000000039000000004000000000410000000042000000004300000000440000000045000000004600000000470000000048000000004900000000500000000051000000005200000000530000000054000000005500000000560000000057000000005800000000590000000060000000006100000000620000000063000000006400000000650000000066000000006700000000680000000069000000007000000000710000000072000000007300000000740000000075000000007600000000770000000078000000007900000000800000000081000000008200000000830000000084000000008500000000860000000087000000008800000000890000000090000000009100000000920000000093000000009400000000950000000096000000009700000000980000000099000000010000000001010000000102000000010300000001040000000105000000010600000001070000000108000000010900000001100000000111000000011200000001130000000114000000011500000001160000000117000000011800000001190000000120000000012100000001220000000123000000012400000001250000000126000000012700000001280000000129000000013000000001310000000132000000013300000001340000000135000000013600000001370000000138000000013900000001400000000141000000014200000001430000000144000000014500000001460000000147000000014800000001490000000150000000015100000001520000000153000000015400000001550000000156000000015700000001580000000159000000016000000001610000000162000000016300000001640000000165000000016600000001670000000168000000016900000001700000000171000000017200000001730000000174000000017500000001760000000177000000017800000001790000000180000000018100000001820000000183000000018400000001850000000186000000018700000001880000000189000000019000000001910000000192000000019300000001940000000195000000019600000001970000000198000000019900000002000000000201000000020200000002030000000204000000020500000002060000000207000000020800000002090000000210000000021100000002120000000213000000021400000002150000000216000000021700000002180000000219000000022000000002210000000222000000022300000002240000000225000000022600000002270000000228000000022900000002300000000231000000023200000002330000000234000000023500000002360000000237000000023800000002390000000240000000024100000002420000000243000000024400000002450000000246000000024700000002480000000249000000025000000002510000000252000000025300000002540000000255000000025600000002570000000258000000025900000002600000000261000000026200000002630000000264000000026500000002660000000267000000026800000002690000000270000000027100000002720000000273000000027400000002750000000276000000027700000002780000000279000000028000000002810000000282000000028300000002840000000285000000028600000002870000000288000000028900000002900000000291000000029200000002930000000294000000029500000002960000000297000000029800000002990000000300000000030100000003020000000303000000030400000003050000000306000000030700000003080000000309000000031000000003110000000312000000031300000003140000000315000000031600000003170000000318000000031900000003200000000321000000032200000003230000000324000000032500000003260000000327000000032800000003290000000330000000033100000003320000000333000000033400000003350000000336000000033700000003380000000339000000034000000003410000000342000000034300000003440000000345000000034600000003470000000348000000034900000003500000000351000000035200000003530000000354000000035500000003560000000357000000035800000003590000000360000000036100000003620000000363000000036400000003650000000366000000036700000003680000000369000000037000000003710000000372000000037300000003740000000375000000037600000003770000000378000000037900000003800000000381000000038200000003830000000384000000038500000003860000000387000000038800000003890000000390000000039100000003920000000393000000039400000003950000000396000000039700000003980000000399000000040000000004010000000402000000040300000004040000000405000000040600000004070000000408000000040900000004100000000411000000041200000004130000000414000000041500000004160... × 10^-20