Question

ͼ£¨1£©ÊÇÓÉÈô¸É¸öСԲȦ¶Ñ³ÉµÄÒ»¸öÐÎÈçÕýÈý½ÇÐεÄͼ°¸£¬×îÉÏÃæÒ»²ãÓÐÒ»¸öԲȦ£¬ÒÔϸ÷²ã¾ù±ÈÉÏÒ»²ã¶àÒ»¸öԲȦ£¬Ò»¹²¶ÑÁËn²ã£®½«Í¼£¨1£©µ¹ÖúóÓëԭͼ£¨1£©Æ´³Éͼ£¨2£©µÄÐÎ×´£¬ÕâÑùÎÒÃÇ¿ÉÒÔËã³öͼ£¨1£©ÖÐËùÓÐԲȦµÄ¸öÊýΪ1+2+3+¡­+n=

n(n+1)

2

£®Èç¹ûͼ£¨1£©ÖеÄԲȦ¹²ÓÐ13²ã£º

£¨1£©ÎÒÃÇ×ÔÉÏÍùÏ£¬ÔÚÿ¸öԲȦÖж¼°´Í¼£¨3£©µÄ·½Ê½ÌîÉÏÒ»´®Á¬ÐøµÄÕýÕûÊý1£¬2£¬3£¬4£¬¡­£¬Ôò×îµ×²ã×î×ó±ßÕâ¸öԲȦÖеÄÊýÊÇ

 

£»
£¨2£©ÎÒÃÇ×ÔÉÏÍùÏ£¬ÔÚÿ¸öԲȦÖж¼°´Í¼£¨4£©µÄ·½Ê½ÌîÉÏÒ»´®Á¬ÐøµÄÕûÊý-23£¬-22£¬-21£¬¡­£¬Çóͼ£¨4£©ÖÐËùÓÐԲȦÖи÷ÊýµÄ¾ø¶ÔÖµÖ®ºÍ£®

Answer 1

¿¼µã£º¹æÂÉÐÍ£ºÍ¼Ðεı仯Àà

רÌ⣺

·ÖÎö£º£¨1£©13²ãʱ×îµ×²ã×î×ó±ßÕâ¸öԲȦÖеÄÊýÊǵÚ12²ãµÄ×îºóÒ»¸öÊý¼Ó1£»
£¨2£©Ê×ÏȼÆËãԲȦµÄ¸öÊý£¬´Ó¶ø·ÖÎö³ö23¸ö¸ºÊýºó£¬ÓÖÓжàÉÙ¸öÕýÊý£®

½â´ð£º½â£º£¨1£©µ±ÓÐ13²ãʱ£¬Í¼Öй²ÓУº1+2+3+¡­+11+12¸öԲȦ£¬
¡à×îµ×²ã×î×ó±ßÕâ¸öԲȦÖеÄÊýÊÇ£º6¡Á12+1=79£»
¹Ê´ð°¸Îª£º79£»

£¨3£©Í¼4ÖÐËùÓÐԲȦÖй²ÓÐ1+2+3+¡­+12=

12¡Á13

2

=78¸öÊý£¬ÆäÖÐ23¸ö¸ºÊý£¬1¸ö0£¬54¸öÕýÊý£¬
ËùÒÔͼ4ÖÐËùÓÐԲȦÖи÷ÊýµÄºÍΪ£º
|-23|+|-22|+¡­+|-1|+0+1+2+¡­+54
=£¨1+2+3+¡­+23£©+£¨1+2+3+¡­+54£©£¬
=276+1485£¬
=1761£®

µãÆÀ£º´ËÌâÖ÷Òª¿¼²éÁËͼÐεı仯À࣬ҪÇóѧÉúͨ¹ý¹Û²ì£¬·ÖÎö¡¢¹éÄÉ·¢ÏÖÆäÖеĹæÂÉ£¬²¢Ó¦Ó÷¢ÏֵĹæÂɽâ¾öÎÊÌ⣮עÒâÁ¬ÐøÕûÊýÏà¼ÓµÄʱºòµÄÕâÖÖ¼ò±ã¼ÆËã·½·¨£®