(+1)+(-2)+(+3)+(+3)+(-4)+.+(+2003)+(-2004)

来源：学生作业帮助网编辑：作业帮时间：2024/11/16 11:47:59

(+1)+(-2)+(+3)+(+3)+(-4)+.+(+2003)+(-2004)
(+1)+(-2)+(+3)+(+3)+(-4)+.+(+2003)+(-2004)

(+1)+(-2)+(+3)+(+3)+(-4)+.+(+2003)+(-2004)
当n为偶数时,
S(n)=1²-2²+3²-4²+…+(-1)^(n-1)×n²
=(1-2)(1+2)+(3-4)(3+4)+…+[(n-1)-n][(n-1)+n]
=-[3+7+11+…+(2n-5)+(2n-1)]（令n=2k）
=-[3+7+11+…+(4k-5)+(4k-1)]
=-(3+4k-1)k/2
=-k(2k+1)
=-n(n+1)/2；
当n为奇数时,
S(n)=1²-2²+3²-4²+…+(-1)^(n-1)×n²
=1²+(-2²+3²)+(-4²+5²)+…+[-(n-1)²+n²]
=1+(-2+3)(2+3)+(-4+5)(4+5)+…+[-(n-1)+n][(n-1)+n]
=1+5+9+…+(2n-5)+(2n-1)]（令n=2k-1）
=1+5+9+…+(4k-7)+(4k-3)]
=(1+4k-3)k/2
=k(2k-1)
=n(n+1)/2
可见,
S(n)=(-1)^(n-1)[n(n+1)]/2

1+2-3-3-3-3=? 1^3+2^3+3^3+...+99^3+100^3 2 1 -2 -3 1,1,1,2,2,2,3,3,3,填三阶幻方 (-1/3)^2除以(-1/3)^3*(1/3)^3除以3^-2*(-3)^0 3题 1、2、3 -1-{(-3)²-[3+(2/3)*(-3/2)]/(-2)} 计算 1,1/2,3/2,3/8,( ),( ) 1+1+2+2+3+3+````````````````````````````+99999 求和Sn=1+(1+3)+(1+3+3^2)+(1+3+3^2+3^3)+.+(1+3+3^2+3^3+...+3^n-1) [(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)]=? 求四阶行列式：2 -1 3 2 3 -3 3 2 3 -1 -1 2 3 -1 3 -1 （2/3+3）(3-2/3x)+(-2/3-1)(1+2/3x) 比较大小(4/3)^1/3,2^2/3,(-2/3)^3,(3/4)^1/2 1+3+2+1+1x2+3 1/(2^3)+1/(2^3+1)+1/(2^3+2)+1/(2^3+3)+...+1/(2^4-1) (-4/3)*(-8+3/2-3/1) -8/3+2/3-3/1*24