1+2+3+4+5+6+7+八一直加到二十的简便方法是什么 1+2+3+4+5+6+7+8+9+10如何用简便方法算出答...
1+2+3+4+5+6+7+8+9\u2026\u2026+100\u7b80\u4fbf\u7b97\u6cd5\u9996\u4f4d\u76f8\u52a0\uff1a
1+100,2+99+\u2026\u202650+51
\u6700\u540e\u662f101*50=5050\u3002
\u5f53\u7136\u5982\u679c\u5b66\u8fc7\u4e86\u9ad8\u65af\u6c42\u548c\uff0c\u76f4\u63a5\u4ee3\u516c\u5f0f\u5c31\u53ef\u4ee5\u4e86\uff1a
\u9ad8\u65af\u6c42\u548c\u516c\u5f0f\u662f\uff1a1+2+3+4+\u2026+n=n(n+1)/2;
\u7b54\u6848\u662f\u4e00\u6837\u7684\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u6587\u5b57\u8868\u8ff0\uff1a\u548c=(\u9996\u9879 + \u672b\u9879\uff09x\u9879\u6570 /2\u6570\u5b66\u8868\u8fbe\uff1a1+2+3+4+\u2026\u2026+ n = (n+1)n /2
\u7ea6\u7ff0\u00b7\u5361\u5c14\u00b7\u5f17\u91cc\u5fb7\u91cc\u5e0c\u00b7\u9ad8\u65af\uff08Johann Carl Friedrich Gauss \uff0c1777\u5e744\u670830\u65e5\uff0d1855\u5e742\u670823\u65e5\uff09\u5fb7\u56fd\u8457\u540d\u6570\u5b66\u5bb6\u3001\u7269\u7406\u5b66\u5bb6\u3001\u5929\u6587\u5b66\u5bb6\u3001\u5927\u5730\u6d4b\u91cf\u5b66\u5bb6\u3002\u662f\u8fd1\u4ee3\u6570\u5b66\u5960\u57fa\u8005\u4e4b\u4e00\uff0c\u9ad8\u65af\u88ab\u8ba4\u4e3a\u662f\u5386\u53f2\u4e0a\u6700\u91cd\u8981\u7684\u6570\u5b66\u5bb6\u4e4b\u4e00\uff0c\u5e76\u4eab\u6709\u201c\u6570\u5b66\u738b\u5b50\u201d\u4e4b\u79f0\u3002
\u9ad8\u65af\u548c\u963f\u57fa\u7c73\u5fb7\u3001\u725b\u987f\u5e76\u5217\u4e3a\u4e16\u754c\u4e09\u5927\u6570\u5b66\u5bb6\u3002\u4e00\u751f\u6210\u5c31\u6781\u4e3a\u4e30\u7855\uff0c\u4ee5\u4ed6\u540d\u5b57\u201c\u9ad8\u65af\u201d\u547d\u540d\u7684\u6210\u679c\u8fbe110\u4e2a\uff0c\u5c5e\u6570\u5b66\u5bb6\u4e2d\u4e4b\u6700\u3002\u4ed6\u5bf9\u6570\u8bba\u3001\u4ee3\u6570\u3001\u7edf\u8ba1\u3001\u5206\u6790\u3001\u5fae\u5206\u51e0\u4f55\u3001\u5927\u5730\u6d4b\u91cf\u5b66\u3001\u5730\u7403\u7269\u7406\u5b66\u3001\u529b\u5b66\u3001\u9759\u7535\u5b66\u3001\u5929\u6587\u5b66\u3001\u77e9\u9635\u7406\u8bba\u548c\u5149\u5b66\u7686\u6709\u8d21\u732e\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u9ad8\u65af\u6c42\u548c
\u7b54\u6848\uff1a55\u3002
\u7b80\u4fbf\u7b97\u6cd5\u5982\u4e0b\uff1a
1+2+3+4+5+6+7+8+9+10\uff1d\uff081+10\uff09\u00d710\u00f72\uff1d11\u00d75\uff1d55
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u52a0\u6cd5\u4ea4\u6362\u5f8b
\u4e24\u4e2a\u52a0\u6570\u4ea4\u6362\u4f4d\u7f6e\uff0c\u548c\u4e0d\u53d8\uff0c\u8fd9\u53eb\u505a\u52a0\u6cd5\u4ea4\u6362\u5f8b\u3002
\u5b57\u6bcd\u516c\u5f0f\uff1aa+b+c=a+c+b
\u9898\u4f8b\uff08\u7b80\u7b97\u8fc7\u7a0b\uff09\uff1a6+18+4
= 6+4+18
= 28
2\u3001\u52a0\u6cd5\u7ed3\u5408\u5f8b
\u5148\u628a\u524d\u4e24\u4e2a\u6570\u76f8\u52a0\uff0c\u6216\u5148\u628a\u540e\u4e24\u4e2a\u6570\u76f8\u52a0\uff0c\u548c\u4e0d\u53d8\u53eb\u505a\u52a0\u6cd5\u7ed3\u5408\u5f8b\u3002
\u5b57\u6bcd\u516c\u5f0f\uff1aa+b+c=a+(b+c)
\u9898\u4f8b\uff08\u7b80\u7b97\u8fc7\u7a0b\uff09\uff1a6+18+2
= 6+(18+2)
= 6+20
= 26
3\u3001\u4e58\u6cd5\u4ea4\u6362\u5f8b\uff1a
\u4e58\u6cd5\u4ea4\u6362\u5f8b\u7684\u6982\u5ff5\u4e3a\uff1a\u4e24\u4e2a\u56e0\u6570\u4ea4\u6362\u4f4d\u7f6e\uff0c\u79ef\u4e0d\u53d8\u3002
\u5b57\u6bcd\u516c\u5f0f\uff1aa\u00d7b=b\u00d7a
\u9898\u4f8b\uff08\u7b80\u7b97\u8fc7\u7a0b\uff09\uff1a12\u00d78
=8\u00d712
=96
4\u3001\u4e58\u6cd5\u7ed3\u5408\u5f8b\uff1a
\u4e58\u6cd5\u7ed3\u5408\u5f8b\u7684\u6982\u5ff5\u4e3a\uff1a\u5148\u4e58\u524d\u4e24\u4e2a\u6570\uff0c\u6216\u5148\u4e58\u540e\u4e24\u4e2a\u6570\uff0c\u79ef\u4e0d\u53d8\u3002
\u5b57\u6bcd\u516c\u5f0f\uff1aa\u00d7b\u00d7c=a\u00d7(b\u00d7c)
\u9898\u4f8b\uff1a30\u00d725\u00d74
=30\u00d7\uff0825\u00d74\uff09
=30 \u00d7100
=3000
5\u3001\u4e58\u6cd5\u5206\u914d\u5f8b\uff1a
\u4e58\u6cd5\u5206\u914d\u5f8b\u7684\u6982\u5ff5\u4e3a\uff1a\u4e24\u4e2a\u6570\u7684\u548c\uff0c\u4e58\u4ee5\u4e00\u4e2a\u6570\uff0c\u53ef\u4ee5\u62c6\u5f00\u6765\u7b97\uff0c\u79ef\u4e0d\u53d8\u3002
\u5b57\u6bcd\u516c\u5f0f\uff1a\uff08a+b\uff09\u00d7c=a\u00d7c+b\u00d7c
\u4f8b\u9898\uff1a\uff082+3\uff09\u00d710
=3\u00d710+2\u00d710
=30+20
=50
1+2+3+4+5+6+7+八一直加到二十
=（1+20）+（2+19）+。。。+（10+11）
=21*10
=210
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绛旓細1+8+6=9+1+5=8+3+4=6+2+7
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