Interesting Numbers Patterns

1. Square numbers of 1, 11, 111, 1111,…..etc. They give a beautiful patterns like this.

2. Another interesting pattern.

7² = 49

67² = 4489

667² = 444889

6667² = 44448889

66667² = 4444488889

666667² = 444444888889

3. Adding consecutive odd numbers.

1 =  1  =    1³

3 + 5 =  8  =   2³

7 + 9 + 11 = 27 = 3³

13 + 15 + 17 + 19 = 64 = 4³

21 + 23 + 25 + 27 + 29 = 125 = 5³

4. Number patterns  

                          ^{9 x 9 + 7 = 88 
                        98 x 9 + 6 = 888
                      987 x 9 + 5 = 8888
                    9876 x 9 + 4 = 88888
                  98765 x 9 + 3 = 888888 
                987654 x 9 + 2 = 8888888
              9876543 x 9 + 1 = 88888888
            98765432 x 9 + 0 = 888888888}

5. Sequential Inputs of 9

^{9 x 9 = 81
99 x 99 = 9801
999 x 999 = 998001}

^{9999 x 9999 = 9998001
99999 x 99999 = 9999800001
999999 x 999999 = 999998000001}

^{9999999 x 9999999 = 99999980000001}

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