-1的n次方乘以n的平方,数列求和

问题描述:

-1的n次方乘以n的平方,数列求和

∵a[n]=(-1)^n*n^2∴S[n]=-1+4-9+16-25+36-...-(2k-1)^2+(2k)^2-...+(-1)^n*n^2(k为正整数)=3+7+11+...+(4k-1)+...+(-1)^n*n^2∵当n=2k-1时,k-1=(n-1)/2∴S[2k-1]=(k-1)[3+4(k-1)-1]/2-(2k-1)^2=(k-1)(2k-1)-(2k-1...