Question

请观察 25=5^2 1225=35^2 112225=335^2 11122225=3335^2 写出表示一般规律的等

Answer 1

设：111...111(n个1 )=x

则：10^n =9x+1

n个1 (n+1)个2

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111...111222...2225

=111...111222...2200 (其中n个1,n个2) +25

=x*10^(n+2) +200x +25

=100x*10^n +200x +25

=100x(10^n+2)+25

=100x(9x+3)+25

=900x^2+300x+25

=(30x)^2+10(30x)+25

=(30x+5)^2

其中：30x=333...3330 (n个3)