计算，1的平方+2的平方+3的平方一直加到100的平方。求简便方法！
\u4e00\u7684\u5e73\u65b9\u52a0\u4e8c\u7684\u5e73\u65b9\u52a0\u4e09\u7684\u5e73\u65b9\u4e00\u76f4\u52a0\u5230\u4e00\u767e\u7684\u5e73\u65b9\u7b49\u4e8e\u591a\u5c11\u89e3\uff1a\u516c\u5f0f\uff1a
1²+2²+3²+....+n²
=1/6 n(n+1)(2n+1)
\u6240\u4ee5
\u53d6n=100\uff0c\u5f97
\u539f\u5f0f=1/6 \u00d7100\u00d7\uff08100+1\uff09\u00d7\uff082\u00d7100+1\uff09
=338350
\u5e73\u65b9\u548c\u516c\u5f0f\uff1a
1^2+2^2+...+n^2=n(n+1)(2n+1)/6
\u8fd9\u4e2a\u516c\u5f0f\u7ed9\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u63a8\u5bfc\u3002\u5982\u4e0b\u56fe\uff0c\u753b\u4e00\u4e2a\u6570\u5b57\u4e09\u89d2\u5f62\uff1a
\u628a1^2\u770b\u4f5c\u4e00\u4e2a1\uff0c2^2\u770b\u4f5c\u4e24\u4e2a2...\u4ee5\u6b64\u7c7b\u63a8\u3002\u6240\u4ee51^2+2^2+...+n^2\u5c31\u662f\u8fd9\u4e2a\u4e09\u89d2\u5f62\u4e2d\u6240\u6709\u6570\u5b57\u4e4b\u548c\u3002
1
2,2
3,3,3
......
n,n,n,...n
\u628a\u5b83\u987a\u65f6\u9488\u65cb\u8f6c120\u5ea6\uff0c\u5219\u5f97\u53e6\u4e00\u4e2a\u56fe\uff0c\u518d\u65cb\u8f6c120\u5ea6\uff0c\u53c8\u5f97\u5230\u7b2c\u4e09\u4e2a\u56fe\uff0c\u628a\u56fe\u4e2d\u5bf9\u5e94\u4f4d\u7f6e\u4e0a\u7684\u6570\u5b57\u76f8\u52a0\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u5c06\u5f97\u5230\u7684\u7b2c\u56db\u4e2a\u56fe\u4e2d\uff0c\u4e09\u89d2\u5f62\u4e2d\u6bcf\u4e2a\u6570\u90fd\u662f2n+1\uff0c\u800c\u4e14\u8fd9\u4e2a\u4e09\u89d2\u5f62\u4e2d\u4e00\u5171\u4f1a\u67091+2+3+...+n=n(n+1)/2\u4e2a\u6570\u3002\u6240\u4ee5\u4e09\u4e2a\u4e09\u89d2\u5f62\u4e2d\u6240\u6709\u6570\u5b57\u4e4b\u548c\u4e3an(n+1)(2n+1)/2,\u800c\u8fd9\u662f\u4e09\u4e2a\u4e09\u89d2\u5f62\u7684\u6570\u5b57\u4e4b\u548c\uff0c\u4e00\u4e2a\u4e09\u89d2\u5f62\u7684\u8bdd\u4e5f\u5c31\u662f\u518d\u9664\u4ee5\u4e09\uff0c\u4e5f\u53731^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6
采纳哦
公式是 1 + 2 + 3 + ...＋n = n(n+1)(2n+1)/6 把n = 100 代入得： n(n+1)(2n+1)/6 = 100×101×201÷6 = 338350 所以 1 + 2 + 3 + ...＋100 = 338350
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