急求【初一奥数题】戳进来题目有图
\u6025\u6c42\u3010\u521d\u4e00\u5965\u6570\u9898\u3011\u6233\u8fdb\u6765\u9898\u76ee\u6709\u56fe.\u7b54\u6848\u662f2015/4028\uff08\u5e94\u8be5\u662f\u5bf9\u7684\uff09
\u8bdd\u8bf4\u9898\u76ee\u4e0a\u7b2c\u4e00\u4e2a\u62ec\u53f7\u91cc\u662f(1-1/ 2\u7684\u4e8c\u6b21)\u5417\uff1f
\u8fc7\u7a0b\uff1a\u539f\u5f0f=\uff081+1/2\uff09\uff081-1/2\uff09\uff081+1/3\uff09\uff081-1/3\uff09\uff081+1/4\uff09\uff081-1/4\uff09....\uff081+1/2013\uff09
\uff081-1/2013\uff09\uff081+1/2014\uff09\uff081-1/2014\uff09\u3010\u5e73\u65b9\u5dee\u516c\u5f0f\u3011
=3/2*1/2*4/3*2/3*5/4*3/4*.....*2014/2013*2012/2013*2015/2014*2013/2014
\u3010\u7ea6\u5206\u540e\u3011=1/2*2015/2014
=2015/4028
1\u3001\u80fd\u770b\u52306\u4e2a\uff0c\u5b9e\u9645\u5171\u670910\u4e2a\u3002
2\u3001\u89c4\u5f8b\u662f\uff1a\u6bcf\u5c42\u6309\u589e\u52a01\u30012\u30013\u30014\u30015\u30016\u30017.....\u589e\u52a0\u3002\u7b2c\u516d\u5c42\u662f\uff1a1+2+3+4+5+6=21\u4e2a\uff0c
\u7b2c\u4e00\u5c42\uff1a1\u4e2a\uff0c\u7b2c\u4e8c\u5c42\uff1a1+2=3\u4e2a\uff0c\u7b2c\u4e09\u5c42\uff1a1+2+3=6\u4e2a\uff0c\u7b2c\u56db\u5c42\uff1a1+2+3+4=10\u4e2a\uff0c\u7b2c\u4e94\u5c42\uff1a1+2+3+4+5=15\u4e2a
\u603b\u6570\uff1a1+3+6+10+15+21=56\uff08\u4e2a\uff09
等式右侧展开:[n(n+1)]^2+2n(n+1)+1
后面那个2n(n+1)+1=2n^2+2n+1=(n^2)+(n^2+2n+1)=n^2+(n+1)^2
n^2+[n*(n+1)]^2+(n+1)^2=[n^2+(n+1)]^2
证：左边=n^2+(n^2)*(n+1)^2+(n+1)^2=(n^2)*(n^2+2n+2)=n^4+(2n^2)*(n+1)=右边
n²+[n(n+1)]²+(n+1)²=[n(n+1)+1]²
证明
n²+[n(n+1)]²+(n+1)²
＝[n(n+1)]²+n²+n²+2n+1
＝[n(n+1)]²+2n(n+1)+1
＝[n(n+1)+1]²
n²+[n(n+1)]²+（n+1)²=[n(n+1)+1]²
绛旓細鍚庨潰閭ｄ釜2n(n+1)+1=2n^2+2n+1=(n^2)+(n^2+2n+1)=n^2+(n+1)^2
绛旓細绛旀鏄2015/4028锛堝簲璇ユ槸瀵圭殑锛夎瘽璇棰樼洰涓婄涓涓嫭鍙烽噷鏄(1-1/ 2鐨勪簩娆)鍚楋紵杩囩▼锛氬師寮=锛1+1/2锛夛紙1-1/2锛夛紙1+1/3锛夛紙1-1/3锛夛紙1+1/4锛夛紙1-1/4锛...锛1+1/2013锛夛紙1-1/2013锛夛紙1+1/2014锛夛紙1-1/2014锛夈愬钩鏂瑰樊鍏紡銆=3/2*1/2*4/3*2/3*5/4*3/4*...*2014...
