简算:(2+4+6+.+2000)-(1+3+5+...+1999) 简算:(1+3+5+7+...99+101)-(2+4+6+8+..+98+100)

问题描述:

简算:(2+4+6+.+2000)-(1+3+5+...+1999) 简算:(1+3+5+7+...99+101)-(2+4+6+8+..+98+100)

(2+4+6+......+2000)-(1+3+5+...+1999)
=(2-1)+(4-3)+(6-5)+……+(2000-1999)=1000

(1+3+5+7+...99+101)-(2+4+6+8+..+98+100)
=(1-2)+(3-4)+(5-6)+……+(99-100)+101=-50+101=51

(1)原式=(2-1)+(4-3)+。。。。+(2000-1999)=1*2000/2=1000
(2)原式=(1-2)+(3-4)+........+(99-100)+101=-1*50+101=51

简算:(2+4+6+.+2000)-(1+3+5+...+1999)
=(2-1)+(4-3)+(6-5)+...+(2000-1999)
=1+1+..+1
=1x1000
=1000
简算:(1+3+5+7+...99+101)-(2+4+6+8+..+98+100)
=1+(3-2)+(5-4)+...+(99-98)+(101-100)
=1+1+..+1
=1+1x100
=101