Question

1-2/1*(1+2)-3/(1+2)(1+2+3)-4/(1+2+3)(1+2+3+4)-…-100/(1+2+…+99)(1+2+…+100)=

急急！

Answer 1

观察式子，1-2/(1x3)-3/(3x6)-4/(6x10)-5/(10x15)-6/(15x21)....... - 99/(4851x4950) - 100/(4950x5050)
=1-2(1x3)-1/(1x2)-2/(3x5)-1/(2x3)-2/(5x7)-.....-1/(49x50)-2/(99x101)
把分母是2的放一起,然后提个2出来，分母是1的放一起。。得到下列式子
注意1/(1x3)这种分出来是(1/1-1/3)x(1/2)

原式= 1-2/(1x3)-2/(3x5)-2/(5x7)-.........-2/(99x101) - 1/(1x2)-1/(2x3)-1/(3x4)-....-1/(49-50)
= 1-2[(1/1-1/3)/2 - (1/3-1/5)/2 - (1/5-1/7)/2 -.....- (1/99-1/101)/2] - [(1/1-1/2) + (1/2-1/3) +......+ (1/49-1/50)]
第一个大括号内提 1/2出来
= 1- (1/1-1/101) - (1/1-1/50)
= 1 - 100/101 - 49/50
= -4899/5050