证明一道题目0x 9 + 1 = 1 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 12
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证明一道题目0x 9 + 1 = 1 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 12
证明一道题目
0x 9 + 1 = 1
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9+10 = 1111111111
证明一道题目0x 9 + 1 = 1 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 12
数学归纳法
如果第k个式子成立,
则第k+1个式子
1...k*9+(k+1)=(1...1(k个1)-k)*10+k*9+(k+1)=1...1(k+1个1)
由第1个式子成立,后面所有式子成立
当然计算器验证也很快