Question

16£®¹Û²ìÏÂÁеÈʽ£º
¢Ù$\frac{1}{1¡Á2}$=1-$\frac{1}{2}$£¬¢Ú$\frac{1}{2¡Á3}$=$\frac{1}{2}$-$\frac{1}{3}$£¬$¢Û\frac{1}{3¡Á4}$=$\frac{1}{3}$-$\frac{1}{4}$£¬¡­
£¨1£©¸ù¾Ý¹æÂÉд³öµÚ5¸öµÈʽ£º$\frac{1}{5¡Á6}$=$\frac{1}{5}$-$\frac{1}{6}$£¬µÚn¸öµÈʽ£º$\frac{1}{n£¨n+1£©}$=$\frac{1}{n}$-$\frac{1}{n+1}$£»
£¨2£©ÀûÓùæÂɼÆË㣺$\frac{1}{1¡Á2}$+$\frac{1}{2¡Á3}$+$\frac{1}{3¡Á4}$+¡­+$\frac{1}{2012¡Á2013}+\frac{1}{2013¡Á2014}+\frac{1}{2014¡Á2015}$£®

Answer 1

·ÖÎö £¨1£©¸ù¾ÝÒÑÖªµÈʽµÃ³öÒ»°ãÐÔ¹æÂÉ£¬Ð´³ö¼´¿É£»
£¨2£©Ô­Ê½ÀûÓòðÏî·¨±äÐΣ¬µÖÏûºÏ²¢¼´¿ÉµÃµ½½á¹û£®

½â´ð ½â£º£¨1£©¸ù¾Ý¹æÂÉд³öµÚ5¸öµÈʽ£º$\frac{1}{5¡Á6}$=$\frac{1}{5}$-$\frac{1}{6}$£¬µÚn¸öµÈʽ£º$\frac{1}{n£¨n+1£©}$=$\frac{1}{n}$-$\frac{1}{n+1}$£»
£¨2£©Ô­Ê½=1-$\frac{1}{2}$+$\frac{1}{2}$-$\frac{1}{3}$+¡­+$\frac{1}{2014}$-$\frac{1}{2015}$
=1-$\frac{1}{2015}$
=$\frac{2014}{2015}$£®
¹Ê´ð°¸Îª£º£¨1£©$\frac{1}{5¡Á6}$=$\frac{1}{5}$-$\frac{1}{6}$£¬$\frac{1}{n£¨n+1£©}$=$\frac{1}{n}$-$\frac{1}{n+1}$£®

µãÆÀ ´ËÌ⿼²éÁËÓÐÀíÊýµÄ»ìºÏÔËË㣬ÊìÁ·ÕÆÎÕÔËËã·¨ÔòÊǽⱾÌâµÄ¹Ø¼ü£®