(1/2+1/3+··1/2010)(1+1/2+1/3··+1/2009)-(1/2+1/3··+1/2009)(1+1/2+1/3··1/2010)等于多少

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(1/2+1/3+··1/2010)(1+1/2+1/3··+1/2009)-(1/2+1/3··+1/2009)(1+1/2+1/3··1/2010)等于多少(1/2+1/3+··1/2010)(1

(1/2+1/3+··1/2010)(1+1/2+1/3··+1/2009)-(1/2+1/3··+1/2009)(1+1/2+1/3··1/2010)等于多少
(1/2+1/3+··1/2010)(1+1/2+1/3··+1/2009)-(1/2+1/3··+1/2009)(1+1/2+1/3··1/2010)等于多少

(1/2+1/3+··1/2010)(1+1/2+1/3··+1/2009)-(1/2+1/3··+1/2009)(1+1/2+1/3··1/2010)等于多少
第一个括号里先+1再-1,也就是变成(1+1/2+1/3+1/4+...+1/2010-1)
式子就变成【(1+1/2+1/3+1/4+...+1/2010)-1】(1+1/2+1/3+...+1/2009)-(1+1/2+1/3+...+1/2010)(1/2+1/3+1/4+...+1/2009)
把前两个乘积按分配律展开,就变成:(1+1/2+1/3+1/4+...+1/2010)(1+1/2+1/3+...+1/2009)-1×(1+1/2+1/3+...+1/2009)-(1+1/2+1/3+...+1/2010)(1/2+1/3+1/4+...+1/2009)
=(1+1/2+1/3+1/4+...+1/2010)(1+1/2+1/3+...+1/2009)-(1+1/2+1/3+...+1/2010)(1/2+1/3+1/4+...+1/2009)-1×(1+1/2+1/3+...+1/2009)
=(1+1/2+1/3+1/4+...+1/2010)【(1+1/2+1/3+...+1/2009)-(1/2+1/3+1/4+...+1/2009)】-1×(1+1/2+1/3+...+1/2009)
=(1+1/2+1/3+1/4+...+1/2010)-(1+1/2+1/3+...+1/2009)
=1/2010

0

(1/2+1/3+··1/2010)(1+1/2+1/3··+1/2009)-(1/2+1/3··+1/2009)(1+1/2+1/3··1/2010)等于多少 2010·(1-1/2)·(1-1/3)·(1-1/4)·…·(1-1/2010) 1、(1+3+5+···+2009+2011)-(2+4+6+···+2010+2012) (-1乘2)+(-1/2乘3)+·······+(-1/2010乘1/2011)等于 (-1)+2+(-3)+4+······+(-2009)+2010+(-2011)=________________________(注意: (1)2010×(1-1/2)×(1-1/3)×(1-1/4)×·········×(1-1/2009)×(1-1/2010) 用简便算法 (2)已知 1/3-1/5=1/3*5*2 那么 1/3*5+1/5*7+1、7*9+···+1、19*21(2)已知 1/3-1/5=1/3*5*2 那么 1/3*5+1/5*7+1、7*9+· 计算:(-1)+(+2)+(-3)+(-4)+.+(-99)+(+100)+.+(-2009)+(+2010)快点··········很急 1+1/(1+2)+1/(1+2+3)+·····+1/(1+2+3+·····+n) 求和 (1/2011-1)(1/2010-1)(1/2009-1)···(1/3-1)(1/2-1) -1*1/2+(-1/2*1/3)+(-1/3*1/4)+···+(-1/2010*1/2011) 计算(1-2分之1)+(2分之1-3分之1)+(3分之1-4分之1)+···+(2009分之1-2010分之1) 秦始皇和汉武帝各自的功劳是?(用1·······2·······3··········来说) 1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3+······+200)=? 判断下列无穷级数的敛散性(1)1+2+3+···+n+···(2)1/(1·2)+1/(2·3)+···+1/n(/n+1)+··· 急·····················1+2+3+...+999=? 计算:(1-1/21)×(1-1/20)×(1-1/19)×(1-1/18)×······(1-1/3)×(1-1/2)(要完整) 2[4/3y—(2/3y—1/2)]=3/4y急·································!1 1 2 3 4 ·····7 ·······10 ········?1 3 5 7 ·····?······?··········290 1 4 9 ·····?······?··········?