1/x-1(x+1)=1/x(x+1),既有1/x(x+1)=1/x-1/(x+1).试用上式计算:(1/1*2)+(1/2*3)+(1/3*4)+…+(1/2001*2002
问题描述:
1/x-1(x+1)=1/x(x+1),既有1/x(x+1)=1/x-1/(x+1).试用上式计算:(1/1*2)+(1/2*3)+(1/3*4)+…+(1/2001*2002
)急的…………………………!
答
(1/1*2)+(1/2*3)+(1/3*4)+…+(1/2001*2002)=1-1/2+1/2-1/3+1/3-1/4+.1/2000-1/2001+1/2001-1/2002=1-1/2002=2001/2002