数学简便计算题（平方差公式） 数学简便计算题
\u6570\u5b66\u8ba1\u7b97\u9898\uff08\u5e73\u65b9\u5dee\u516c\u5f0f\uff09(1+1/2)(1-1/2)(1+1/3)(1-1/3)\u2026\u2026\uff081+1/2011\uff09(1-1/2011()(1+1/2012)(1-1/2012)
=3/2\u00d71/2\u00d74/3\u00d72/3\u00d7\u2026\u2026\u00d72012/2011\u00d72010/2011\u00d72013/2012\u00d72011/2012
=\uff08\u524d\u540e\u76f8\u4e92\u62b5\u6d88\uff091/2\u00d72013/2012
=2013/4024
\u5e0c\u671b\u6709\u5e2e\u52a9\uff0c\u53ea\u8981\u7262\u8bb0\u516c\u5f0f\u5c31\u53ef\u4ee5\u5f88\u597d\u5229\u7528
1\u9898\uff1a\u7531\u8ba1\u7b97\u53ef\u77e5362+186=548\uff0c\u5219\u5c06362\u770b\u505aa\uff0c186\u770b\u505ab\uff0c\u5219548\u4e3aa+b\uff0c\u90a3\u4e48\u8be5\u5f0f\u5c31\u7b49\u4e8e\uff1a
a\uff08a+b\uff09-b/a\u00b7\uff08a+b\uff09\u00b7\uff08a-1\uff09=\uff08a+b\uff09[a-b/a\u00b7\uff08a-1\uff09]=\uff08a+b\uff09\uff08a-b+b/a\uff09\u5219
\u539f\u5f0f=548\u00d7\uff08362-186+186/362\uff09=548\u00d7\uff08176+1/2+5/362\uff09
\u5219\u8fd9\u4e2a\u4e3a\u6700\u7b80\uff0c\u5269\u4e0b\u7684\u5c31\u662f\u786c\u7b97\u4e86\u3002
2\u9898\uff1a\u539f\u5f0f=\uff0818+1)(18-1)/18 ,\u7531\u5e73\u65b9\u5dee\u516c\u5f0f\uff1aa²-b²=\uff08a+b\uff09\uff08a-b\uff09\u5f97
\u539f\u5f0f=\uff0818²-1\uff09/18=18-1/18 \u7136\u540e\u81ea\u5df1\u4f1a\u7b97\u4e86\u5427
3\u9898\u81ea\u5df1\u53ef\u4ee5\u5c1d\u8bd5\u4e0b\uff0c\u4e00\u65f6\u6211\u8fd8\u6ca1\u505a\u51fa\u6765\uff0c\u4f60\u53ef\u4ee5\u53bb\u7f51\u4e0a\u67e5\u4e0b\u5206\u89e3\u56e0\u5f0f\uff0c\u516b\u4e0b\u77e5\u8bc6\uff0c\u7528\u90a3\u4e2a\u5c31\u4f1a\u505a\u51fa\u6765\u7684
\u5e0c\u671b\u80fd\u5e2e\u52a9\u5230\u4f60\uff0c\u624b\u6253\u5f88\u8f9b\u82e6\uff0c\u52ff\u590d\u5236\u3001\u3001\u3001\u3001
一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)
=（1-1/2）（1+1/2）（1-1/3）（1+1/3）。。。（1-1/100）（1+1/100）
=1/2x3/2x2/3x...x99/100x101/100
=1/2x101/100
=101/200
二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=2*(1-1/2)、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=2*(1-1/2²)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=。。
=2*（1-1/2^16）+1/2^15
=2-1/2^15+1/2^15
=2
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1. （1+1/2）（1-1/2）（1+1/3）（1-1/3）……（1-1/99）（1+1/100）（1-1/100）
=3/2×1/2×4/3×2/3×5/4×3/4……×98/99×101/100×99/100
=1/2×101/100= 101/200
2.
给个思路你
(1)
[1-(1/2)²][1-(1/3)²].......[1-(1/99)²][1-(1/100)²]
(a+b)(a-b)=a的平方-b的平方
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