计算:1/2+1/3*4+1/5*6+1/7*8+1/9*10+.+1/2003*2004+1/2005*2006=?
问题描述:
计算:1/2+1/3*4+1/5*6+1/7*8+1/9*10+.+1/2003*2004+1/2005*2006=?
答
=1/2+4/3+6/5+---+2006/2005
=1/2+(2006/2-1)+1/3+1/5+---1/2005
=1002+2008(1/(3*2005)+1/(5*2003)+--+1/1003*1005))
=1002+2008(0.000166251+-------+0.000000992)
=1002+2008*(0.000166251+0.000000992)/2*(1002/2)
=1002+2008*0.004319121
=1086.123394