1*3分之2+3*5分之2+5*7分2+.2001*2003分之2+2003*2005分之2谢谢大家
问题描述:
1*3分之2+3*5分之2+5*7分2+.2001*2003分之2+2003*2005分之2谢谢大家
答
2/3+2/3*5+2/5*7+...+2/2001*2003+2/2003*2005
=1-1/3+1/3-1/5+1/5-1/7+...+1/2001-1/2003+1/2003-1/2005
=1-1/2005
=2004/2005
答
如果式子是
2/(1×3)+2/(3×5)+2/(5×7)+.+2/(2001×2003)+2/(2003×2005)
那么原式=2×[1/(1×3)+1/(3×5)+1/(5×7)+.+1/(2001×2003)+1/(2003×2005)]
=2×1/2×(1-1/3+1/3-1/5+1/5-1/7+.+1/2001-1/2003+1/2003-1/2005)
=1-1/3+1/3-1/5+1/5-1/7+.+1/2001-1/2003+1/2003-1/2005)
=1-1/2005
=2004/2005