12345…n的平方和 1+2的平方+3的平方+ +n的平方，和怎么计算
\u75af\u72c2\u6570\u5b66\uff1a1\u30012\u30013\u30014\u30015\u3001\u2026\u2026\u202619856\u7684\u5e73\u65b9\u548c\u662f\u51e0\uff1f 1\u30012\u30013\u30014\u30015\u3001\u2026\u2026\u2026n\u7684\u5e73\u65b9\u548c\u662f\u51e0\uff1f\u5e73\u65b9\u548c\u516c\u5f0fn(n+1)(2n+1)/6 \u3000\u3000
\u53731^2+2^2+3^2+\u2026+n^2=n(n+1)(2n+1)/6 (\u6ce8\uff1an^2=n\u7684\u5e73\u65b9)
\u6839\u636e\u516c\u5f0f\uff0c1\u30012\u30013\u30014\u30015\u3001\u2026\u2026\u202619856\u7684\u5e73\u65b9\u548c\u662f2609677525016
1²+2²+3²+...+n²=n(n+1)(2n+1)/6.
\u63a8\u7406\u5982\u4e0b:
2³-1³=3\u00d71²+3\u00d71+1
3³-2³=3\u00d72²+3\u00d72+1
4³-3³=3\u00d73²+3\u00d72+1
... ...
(n+1)³-n³=3n²+3n+1
\u4ee5\u4e0an\u4e2a\u5f0f\u5b50\u76f8\u52a0\uff0c\u5f97
(n+1)³-1=3(1²+2²+3²+...+n²)+3(1+2+3+...+n)+(1+1+1+...+1)
\u5373(n+1)³-1=3(1²+2²+3²+...+n²)+3[n(n+1)/2]+n
\u22343S=(n+1)³-1-3n(n+1)/2-(n+1)
\u5373S=n(n+1)(2n+1)/6\u3002
\u6269\u5c55\u8d44\u6599
\u5e73\u65b9\u548c\u76f8\u5173\u516c\u5f0f\uff1a
\uff081\uff091+2+3+.+n=n(n+1)/2
\uff082\uff091^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6
\uff083\uff091\u00d72\uff0b2\u00d73\uff0b3\u00d74\uff0b4\u00d75\uff0b\u2026\uff0bn(n\uff0b1)
\uff1d(1^2+1)+(2^2+2)+(3^2+2)+...+(n^2+n)
=(1^2+2^2+...+n^2)+(1+2+3+.+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)
n×（n+1）x（2n+1）
÷6
绛旓細5.12346^2-12345x12347 =12346²-(12346-1)*(12346+1)=12346²-12346²+1 =1 6.2007^2-4014X2008+2008^2 =2007²-2*2007*2008+2008²=(2007-2008)²=1 7.(2+1)(2^2+1)(2^4+1)鈥2^2^n+1]=(2^2^n)+1)(2^2^n-1)=4^2^n-1 =...
绛旓細12345鏄剧劧鏄棤鐞嗘暟鐨勫钩鏂 浣跨敤璁＄畻鍣ㄥ緱鍒 鏍瑰彿12345绾︾瓑浜111.108 鍗虫璐111.108鐨勫钩鏂 閮芥槸绾︾瓑浜12345鐨勫钩鏂鏍
绛旓細x=10^(2n+4)+10^(n+3)+50 =10^4*10^2n+10^3*10^n+50 璁10^n=k鎵浠 x=10^4k^2+10^3k+50 鎵浠 2:12345=(111+a)(111-b)=12321-ab+111(a-b)鎵浠34+ab=111(a-b) 鍥犱负34+ab>0鎵浠111(a-b)>0 鎵浠>b 鎵浠 3:璁緓^2+x-n=(x-a)(x-b) a,b涓烘暣鏁帮紝鎵浠...
绛旓細骞虫柟宸叕寮忥紝(123456-123455)(123456+123455)=246911
绛旓細绗n骞12345鈥 鑰佽娊鐜嘺a2a3a5a鈥 鏂拌娊鐜0aa2a3a鈥 鎬昏娊鐜嘺2a3a5a8a鈥 鐓ц繖鏍蜂笅鍘,绗8骞磋佽娊鏁颁笌鎬昏娊鏁扮殑姣斿间负 ___ (绮剧‘鍒0.001). 13.(4鍒)鑻鐨勫间娇寰梮2+4x+a=(x+2)2锕1鎴愮珛,鍒檃鐨勫间负 ___ . 绛旀: 7. 鑰冪偣:闆舵寚鏁板箓;鏈夌悊鏁扮殑涔樻柟銆1923992 涓撻:璁＄畻棰樸 鍒嗘瀽:(1)鏍规嵁闆舵寚鏁...
绛旓細3鐨勭珛鏂规牴1.4422 -2鐨勫钩鏂鏍;1.4142i鏄櫄鏁 1234鐨勫钩鏂规牴;35.1283 1200鐨勭珛鏂规牴;10.6266 8955鐨勫钩鏂规牴;94.6309 12345鐨勭珛鏂规牴;23.1116 800鐨勫钩鏂规牴;28.2843 22/5鐨勭珛鏂规牴;1.6386 0.58鐨勫钩鏂规牴;0.7616 -0.432鐨勭珛鏂规牴;-0.7560 18鐨勫钩鏂规牴鍜35鐨勭珛鏂规牴;4.2426 3.2711 6鐨勫钩鏂规牴;2....
绛旓細12345骞虫柟鍘樼背 = 12345 梅 10000骞虫柟绫 = 1.2345骞虫柟绫 甯屾湜鎴戠殑鍥炵瓟瀵规偍鏈夊府鍔╋紝婊℃剰璇烽噰绾筹紝璋㈣阿銆
绛旓細銆13銆戞牴鎹钩鏂瑰樊鍏紡 m鐨勫钩鏂-n鐨勫钩鏂=锛坢-n锛夛紙m+n锛=6 鍥犱负m-n=2 鎵浠+n=3 銆14銆4.3*10鐨-6娆℃柟 銆15銆戯紙x-a锛²-1=x²-2ax+a²-1 鍗筹細-2a=-6涓巃²-1=8 瑙ｅ緱锛歛=3 閲嶇偣鏄-2a=-6杩欎釜寰堥噸瑕 銆16銆戠湅涓嶆竻 銆17銆戝師寮=12345²-(...
绛旓細34锛庡鍥8锛岃嫢灏8涓浉鍚岀殑灏忔鏂逛綋鎷兼垚涓涓ぇ姝ｆ柟浣擄紝鍒欏ぇ姝ｆ柟浣撶殑琛ㄩ潰绉瘮鍘熸潵鐨8涓皬姝ｆ柟浣撹〃闈㈢Н鐨勫拰灏96骞虫柟鍘樼背锛屽垯灏忔鏂逛綋鐨勬１闀挎槸 鍘樼背銆傚浘5 鍥6 鍥7 鍥8 35锛庣敳涔欎袱鍏徃杩戜笁骞寸殑鍒╂鼎濡傚浘9鎵绀猴紝鍒 鍏徃鐨勬晥鐩婃洿濂姐傦紙濉"鐢"鎴"涔"锛夊浘9 36锛庝竴鍧椾笁瑙掑舰鐜荤拑涓嶅皬...
绛旓細闄愬惊鐜皬鏁板寲涓哄垎鏁扮殑閫氱敤鏂规硶锛氱涓姝ユ槸灏嗗皬鏁板垎鎴愪袱閮ㄥ垎锛屼笉寰幆鍜屽惊鐜儴鍒嗭細0.锛345寰幆锛=0.12锛堜笉寰幆閮ㄥ垎锛+0.锛堝惊鐜儴鍒嗭級绗簩姝ワ紝灏嗕袱閮ㄥ垎鍒嗘暟鍖 =12/100+345/99900 =12*999/99900+345/99900 =(12*999+345)/99900 =(12*1000-12+345)/99900 =(12345-12)/99900锛涘悓鐞嗕綘鐨勪妇渚...
