按如图方式作正方形和等腰直角三角形.若第一个正方形的边长AB=1,第一个正方形与第一个等腰直角三角形的 如图所示,在正方形上连接等腰直角三角形和正方形,无限重复同一...
\uff082013?\u8425\u53e3\uff09\u6309\u5982\u56fe\u65b9\u5f0f\u4f5c\u6b63\u65b9\u5f62\u548c\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\uff0e\u82e5\u7b2c\u4e00\u4e2a\u6b63\u65b9\u5f62\u7684\u8fb9\u957fAB=1\uff0c\u7b2c\u4e00\u4e2a\u6b63\u65b9\u5f62\u4e0e\u7b2c\u4e00\u4e2a\u7b49\u2235\u7b2c\u4e00\u4e2a\u6b63\u65b9\u5f62\u7684\u8fb9\u957f\u4e3a1\uff0c\u7b2c2\u4e2a\u6b63\u65b9\u5f62\u7684\u8fb9\u957f\u4e3a\uff0822\uff091=22\uff0c\u7b2c3\u4e2a\u6b63\u65b9\u5f62\u7684\u8fb9\u957f\u4e3a\uff0822\uff092=12\uff0c\u2026\uff0c\u7b2cn\u4e2a\u6b63\u65b9\u5f62\u7684\u8fb9\u957f\u4e3a\uff0822\uff09n-1\uff0c\u2234\u7b2cn\u4e2a\u6b63\u65b9\u5f62\u7684\u9762\u79ef\u4e3a\uff1a[\uff0822\uff092]n-1=12n?1\uff0c\u5219\u7b2cn\u4e2a\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u4e3a\uff1a12n?1\u00d714=12n+1\uff0c\u6545\u7b2cn\u4e2a\u6b63\u65b9\u5f62\u4e0e\u7b2cn\u4e2a\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u548cSn=12n?1+<table cellpaddi
\u4e0b\u4e00\u4e2a\u6b63\u65b9\u5f62\u9762\u79ef\u4e3a\u4e0a\u4e00\u4e2a\u6b63\u65b9\u5f62\u9762\u79ef\u768412\uff0c\u4e0b\u4e00\u4e2a\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\u9762\u79ef\u4e3a\u4e0a\u4e00\u4e2a\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\u9762\u79ef\u768412\uff0c\uff081\uff09S1=1\u00d71+12\u00d722\u00d722=54\uff0c\u2234S2=12+12\u00d712\u00d722\u00d722=58\uff0cS3=516\uff0cS4=532\uff0e\uff082\uff09\u6839\u636e\uff081\uff09\u7684\u6c42\u89e3\uff0c\u603b\u7ed3\u89c4\u5f8b\uff1aSn=12Sn-1\uff0c\u8ba1\u7b97\u5f97S1+S2=158\uff1d5\u00d738\uff0cS1+S2+S3=3516\uff1d5\u00d7716\uff0cS1+S2+
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