数学老师出了一道计算题,小明一看就吓住了 这么多数这么算呢|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2012-1/2011|+|1/2013-1/2012|.
2019-04-15
数学老师出了一道计算题,小明一看就吓住了 这么多数这么算呢
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2012-1/2011|+|1/2013-1/2012|.
优质解答
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2012-1/2011|+|1/2013-1/2012|.=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.+1/2011-1/2012+1/2012-1/2013=1-1/2013=2012/2013
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2012-1/2011|+|1/2013-1/2012|.=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.+1/2011-1/2012+1/2012-1/2013=1-1/2013=2012/2013