1+2+3+4+5+6+7+8+9一直加到100等于多少？ 小明问妈妈:1+2+3+4+5+6+7+8+9加到100等于...
1+2+3+4+5+6+7+8+9\u4e00\u76f4\u52a0\u5230100\u7b49\u4e8e\u591a\u5c11\uff1f1+2+3+4+5+6+7+8+9\u4e00\u76f4\u52a0\u5230100
\uff1d\uff081\uff0b100\uff09\u00d7100\u00f72
\uff1d101\u00d7100\u00f72
\uff1d10100\u00f72
\uff1d5050
\u5982\u679c\u6709\u5e2e\u5230\u60a8
\u8bf7\u7ed9\u4e88\u597d\u8bc4
\u8c22\u8c22\u62c9#^_^#\u795d\u60a8\u6109\u5feb
\u7b97\u6cd5\u4e00\uff08\u627e\u89c4\u5f8b\uff09\u30011+2+3+...+10 \u5341\u4e2a\u6570\u76f8\u52a0\uff0c\u53d61+9\uff0c2+8\uff0c3+7\uff0c4+6\uff0c\u5269\u4e0b5\u4e0e10\uff0c\u548c55
11+12+13+...+20 \u5341\u4e2a\u6570\u76f8\u52a0\uff0c10\u4e2a10\u52a055\uff0c\u548c155
21+22+23+...+30 \u5341\u4e2a\u6570\u76f8\u52a0\uff0c10\u4e2a20\u52a055\uff0c\u548c255
... ...
\u6240\u4ee5 1+2+3+...+100=55+155+255+...+955=(100+200+300+...+900)+55\u00d710=45\u00d7100+55\u00d710=4500+550=5050
\u7b97\u6cd5\u4e8c\uff08\u7b80\u4fbf\u65b9\u6cd5\uff09\u30011+2+3+...+100
=1+99+2+98+3+97+...+54+56+55+100
=100\u00d754+55+100
=5050
\u7b97\u6cd5\u4e09\u3010\u5229\u7528\u516c\u5f0f 1+2+3+...+n=n\u00d7(n+1)\u00f72\u3011\u3001
\u5f97 1+2+3+...+100
=100\u00d7(100+1)\u00f72
=50\u00d7101
=5050
1+2+3+……+100
=(1+100)+(2+99)+……+(50+51)
=101×50
=5050
或者
1+2+3+……+100
=(1+99)+(2+98)+……+(49+51)+50+100
=100×49+50+100
=100×50+50
=5000+50
=5050
1+2+3+4+5+6+7+8+9......+98+99+100=5050
5050。。
(1+100)x00除以2
101x100除以2
5050
=（1+100）+（2+99）+（3+98）+……+（47+54）+（48+53）+（49+52）+（50+51）
=101+101+101+……+101
=101×50
=5050
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