用数学归纳法证明:(n+1)^2+(n+2)^2+……(n+n)^2=n(2n+1)(7n+1)/6就是第Ⅱ步中n=k+1时怎么写_数学解答

用数学归纳法证明:(n+1)^2+(n+2)^2+……(n+n)^2=n(2n+1)(7n+1)/6
就是第Ⅱ步中n=k+1时怎么写

人气：407 ℃　时间：2020-06-21 02:23:29

解答

n^2+2n+1+n^2+4n+4+……+4n^2=(n+3)n^2+(1+n-1)n(n-1)+1+4+9+16+25+……+(n-1)^2
=(n+3)n^2+(n-1)n^2+1+4+9+16+25+……+(n-1)^2
=后面呢(14n^3+9n^2+n)/6=n(2n+1)(7n+1)/6