求大神告诉我这道题的解题思路!

2024-12-27 03:49:51
推荐回答(2个)
回答1:

m是常数,[2i-(m+1)]^2平方开出来,4i^2,i从1到m,平方和公式,4i乘以(m+1),i从1到m,等差求和公式,(m+1)^2常数,乘以m项,最后加起来

回答2:

解:
(2i-1-M)²=4i²-4(M+1)i+(M+1)²
M
∑ (2i-1-M)²
i=1
=4(1²+2²+...+M²)-4(M+1)(1+2+...+M)+M(M+1)²
=4M(M+1)(2M+1)/6 -4(M+1)[M(M+1)/2] +M(M+1)²
=⅔M(M+1)(2M+1) -2M(M+1)²+M(M+1)²
=⅔M(M+1)(2M+1) -M(M+1)²
=M(M+1)[⅔(2M+1)-(M+1)]
=⅓(M-1)M(M+1)