Prove that (the number of 9s are the same); is the sum of the digits of the number .

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- Apr 7th 2008, 02:39 AMjames_bondSum of the digits
Prove that (the number of 9s are the same); is the sum of the digits of the number .

- Apr 7th 2008, 04:50 AMSoroban
Hello, James!

Quote:

Prove that . . . the number of 9s is the same.

is the sum of the digits of the number .

. . Then: .

Since , then: .

. . That is: .

This is the number "moved" places to the left, plus a 1.

. . It contains 9's and an 8.

Therefore: .