Numbers 900,000,000,000s

900,000,000,090 & 987,654,321,098

[Math.]

1×8+1 = 9

12×8+2 = 98

123×8+3 = 987

1,234×8+4 = 9,876

12,345×8+5 = 98,765

123,456×8+6 = 987,654

1,234,567×8+7 = 9,876,543

12,345,678×8+8 = 98,765,432

123,456,789×8+9 = 987,654,321

1,234,567,890×8+90 = 9,876,543,210

      (start of a new cycle)

12,345,678,901×8+901 = 98,765,432,109

123,456,789,012×8+9,002 = 987,654,321,098

1,234,567,890,123×8+90,003 = 9,876,543,210,987

12,345,678,901,234×8+900,004 = 98,765,432,109,876

123,456,789,012,345×8+9,000,005 = 987,654,321,098,765

1,234,567,890,123,456×8+90,000,006 = 9,876,543,210,987,654

12,345,678,901,234,567×8+900,000,007 = 98,765,432,109,876,543

123,456,789,012,345,678×8+9,000,000,008 = 987,654,321,098,765,432

1,234,567,890,123,456,789×8+90,000,000,009 = 9,876,543,210,987,654,321

12,345,678,901,234,567,890×8+ 900,000,000,090 = 98,765,432,109,876,543,210

...      (end of cycle) 

 

900,132,255,009   

[Math.]    Sum of the first 1377 cube numbers:

13+…+13773 = 900,132,255,009 = (1+…+1377)2 = 948,7532.

 

902,503,655,185

[Math.]   Two consecutive sums of consecutive square numbers:

902,503,655,185 = 693782+…+695642 = 695652+…+697502.

 

902,748,917,161   

[Math.]    Sum of the first 1378 cube numbers:

13+…+13783 = 902,748,917,161 = (1+…+1378)2 = 950,1312.

 

905,371,280,100   

[Math.]    Sum of the first 1379 cube numbers:

13+…+13793 = 905,371,280,100 = (1+…+1379)2 = 951,5102.

 

907,401,035,776   

[Math.]  (Sequence of numbers (10n–24), n ³ 3).

9762 = 952,576; 9763 = 929,714,176 and 9764 = 907,401,035,776.

 

907,999,352,100   

[Math.]    Sum of the first 1380 cube numbers:

13+…+13803 = 907,999,352,100 = (1+…+1380)2 = 952,8902.