(1-1/2+1/3-1/4+...+1/2011-1/2012)/(1/(1+2013)+1/(2+2014)+.1/

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/08 11:05:25

(1-1/2+1/3-1/4+...+1/2011-1/2012)/(1/(1+2013)+1/(2+2014)+.1/（1006+3018）)
等于多少?谢谢

先看分子部分,把它按照正负分成两块,第一块1+1/3+1/5+1/7+...+1/2009+1/2011,用A来表示
第二块-1/2-1/4-1/6-..-1/2010-1/2012,用B来表示,对B中的每一个负数都可以换种表达方式
即-1/2=1/2-1 -1/4=1/4-1/2 -1/6=1/6-1/3 . -1/2010=1/2010-1/1005 1/2012=1/2012-1/1006;
则B=1/2-1 +1/4-1/2 + 1/6-1/3 +...+1/2010-1/1005 +1/2012-1/1006
=1/2+1/4+1/6+...1/2010+1/2012 -(1+1/2+1/3+...1/1005+1/1006)
用B1来表示1/2+1/4+1/6+...1/2010+1/2012,B2来表示(1+1/2+1/3+...1/1005+1/1006)
则B=B1-B2
而A+B1=1+1/3+1/5+1/7+...+1/2009+1/2011 + 1/2+1/4+1/6+...+1/2010+1/2012
=1+1/2+1/3+.1/1005+1/1006+1/1007+1/1008+.+1/2010+1/2012=C用C来表示
A+B1-B2=C-B2=1/1007+1/1008+.+1/2010+1/2012 用D来表示所以分子=D
再看分母:
原分母可写成 1/2014+1/2016+1/2018+.+1/4024,提出公因子1/2可得
=1/2(1/1007+1/1008+.+1/2010+1/2012)
=1/2*D
所以分子/分母=D/(1/2D)=2

计算：1/(1*3)+1/(2*4)+1/(3*5)+...+1/(2011*2013)+1/(2012 *2014) (2013/1-1)(2012/1-1)(2011/1-1).(3/1-1)(2/1-1) |1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2012-1/2011|+|1/2013-1/20 计算:1/1*3+1/2*4+1/3*5+…+1/2011*2013+1/2012*2014 1/1×2+1/2×3+1/3×4+…+1/2010×2011+1/2012×2013 |1\2-1| + |1\3-1\2| + |1\4-1\3| +.+ |1\2014-1\2013| |1/2-1|+|1/3-1/2|+|1/4-1/3|+.+|1/2014-1/2013| |1/2014-1/2013|+|1/2013-1/2012|+|1/2012+1/2011|-|1/2011-1/20 (-1*2/1)+(-1/2*1/3)+(-1/3*1/4)+…+(-1/2012*1/2013) (1/2013×1/2012×1/2011×…×1/2×1)∧2014×(2013×2012×2011×…×2×1)∧2 计算（1-1/2)(1/3-1)(1-1/4)(1/5-1)...(1/2013-1)(1-1/2014) |1/2013-1/2012|+ |1/2012-1/2011|+|1/2011-1/2010|-|1/2010-1/2