已知 Iab-2I+Ib-1I=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+200
已知 Iab-2I+Ib-1I=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2001)(b+2001)等于多少
赞 qiuyiliang 幼苗
共回答了16个问题采纳率：93.8% 举报
因为 Iab-2I+Ib-1I=0 所以b=1 a=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2001)(b+2001)
=1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003
=1-1/2+1/2-1/3+1/3-1/4+1/4...+1/2002-1/2003
=1-1/2003
=2002/2003
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2001)(b+2001)
=1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003
=1-1/2+1/2-1/3+1/3-1/4+1/4...+1/2002-1/2003
=1-1/2003
=2002/2003
1年前
3
JUMMY13579 幼苗
共回答了2个问题 举报
等于2002/2003
由前式可得a=2,b=1;则原式化为:
1/(2*1)1/(3*2)+1/(4*3)+……+1/(2003*2002)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2002-1/2003
=1-1/2003
=2002/2003.
由前式可得a=2,b=1;则原式化为:
1/(2*1)1/(3*2)+1/(4*3)+……+1/(2003*2002)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2002-1/2003
=1-1/2003
=2002/2003.
1年前
1
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