1/(21*2)+1/(2*3)···+1/(2002*2003)+1/(2003*2004)+1/(2004*2005)谢谢了,

问题描述:

1/(21*2)+1/(2*3)···+1/(2002*2003)+1/(2003*2004)+1/(2004*2005)谢谢了,
这是一个计算题

原式=(1-1/2)+(1/2-1/3)+···+(1/2002-1/2003)+(1/2003-1/2004)+(1/2004-1/2005) =1-1/2+1/2-1/3+···+1/2002-1/2003+1/2003-1/2004+1/2004-1/2005 =1-1/2005 =2004/2005