2022蹇呬慨浜旂浜岀珷鏁板鐭ヨ瘑鐐规€荤粨
鏁板璇捐鏈変竴瀹氱殑閫熷害瀛︿範锛屾參鑵捐吘鐨勫涔犳槸璁粌涓嶅嚭鎬濈淮閫熷害锛岃繖灏辫姹傚湪鏁板瀛︿範涓竴瀹氳鏈夎妭濂忥紝杩欐牱涔呰€屼箙涔嬶紝鎬濈淮鐨勬晱鎹锋€у拰鏁板鑳藉姏浼氶€愭鎻愰珮銆備笅闈㈡槸灏忕紪鏁寸悊鐨勶紝浠呬緵鍙傝€冨笇鏈涜兘澶熷府鍔╁埌澶у銆?/p>
蹇呬慨浜旂浜岀珷鏁板鐭ヨ瘑鐐规€荤粨
1.鏁板垪姒傚康
鈶犳暟鍒楁槸涓€绉嶇壒娈婄殑鍑芥暟銆傚叾鐗规畩鎬т富瑕佽〃鐜板湪鍏跺畾涔夊煙鍜屽€煎煙涓娿€傛暟鍒楀彲浠ョ湅浣滀竴涓畾涔夊煙涓烘鏁存暟闆哊x鎴栧叾鏈夐檺瀛愰泦{1锛?锛?锛屸€︼紝n}鐨勫嚱鏁帮紝鍏朵腑鐨剓1锛?锛?锛屸€︼紝n}涓嶈兘鐪佺暐銆?/p>
鈶＄敤鍑芥暟鐨勮鐐硅璇嗘暟鍒楁槸閲嶈鐨勬€濇兂鏂规硶锛屼竴鑸儏鍐典笅鍑芥暟鏈変笁绉嶈〃绀烘柟娉曪紝鏁板垪涔熶笉渚嬪锛岄€氬父涔熸湁涓夌琛ㄧず鏂规硶锛歛.鍒楄〃娉?b銆傚浘鍍忔硶;c.瑙ｆ瀽娉曘€傚叾涓В鏋愭硶鍖呮嫭浠ラ€氶」鍏紡缁欏嚭鏁板垪鍜屼互閫掓帹鍏紡缁欏嚭鏁板垪銆?/p>
鈶㈠嚱鏁颁笉涓€瀹氭湁瑙ｆ瀽寮忥紝鍚屾牱鏁板垪涔熷苟闈為兘鏈夐€氶」鍏紡銆?/p>
绛夊樊鏁板垪
1.绛夊樊鏁板垪閫氶」鍏紡
an=a1+(n-1)d
n=1鏃禷1=S1
n鈮?鏃禷n=Sn-Sn-1
an=kn+b(k,b涓哄父鏁?鎺ㄥ杩囩▼锛歛n=dn+a1-d浠=k锛宎1-d=b鍒欏緱鍒癮n=kn+b
2.绛夊樊涓」
鐢变笁涓暟a锛孉锛宐缁勬垚鐨勭瓑宸暟鍒楀彲浠ュ牚绉版渶绠€鍗曠殑绛夊樊鏁板垪銆傝繖鏃讹紝A鍙仛a涓巄鐨勭瓑宸腑椤?arithmeticmean)銆?/p>
鏈夊叧绯伙細A=(a+b)梅2
3.鍓峮椤瑰拰
鍊掑簭鐩稿姞娉曟帹瀵煎墠n椤瑰拰鍏紡锛?/p>
Sn=a1+a2+a3+路路路路路+an
=a1+(a1+d)+(a1+2d)+路路路路路路+[a1+(n-1)d]鈶?/p>
Sn=an+an-1+an-2+路路路路路路+a1
=an+(an-d)+(an-2d)+路路路路路路+[an-(n-1)d]鈶?/p>
鐢扁憼+鈶″緱2Sn=(a1+an)+(a1+an)+路路路路路路+(a1+an)(n涓?=n(a1+an)
鈭碨n=n(a1+an)梅2
绛夊樊鏁板垪鐨勫墠n椤瑰拰绛変簬棣栨湯涓ら」鐨勫拰涓庨」鏁颁箻绉殑涓€鍗婏細
Sn=n(a1+an)梅2=na1+n(n-1)d梅2
Sn=dn2梅2+n(a1-d梅2)
浜﹀彲寰?/p>
a1=2sn梅n-an=[sn-n(n-1)d梅2]梅n
an=2sn梅n-a1
鏈夎叮鐨勬槸S2n-1=(2n-1)an锛孲2n+1=(2n+1)an+1
4.绛夊樊鏁板垪鎬ц川
涓€銆佷换鎰忎袱椤筧m锛宎n鐨勫叧绯讳负锛?/p>
an=am+(n-m)d
瀹冨彲浠ョ湅浣滅瓑宸暟鍒楀箍涔夌殑閫氶」鍏紡銆?/p>
浜屻€佷粠绛夊樊鏁板垪鐨勫畾涔夈€侀€氶」鍏紡锛屽墠n椤瑰拰鍏紡杩樺彲鎺ㄥ嚭锛?/p>
a1+an=a2+an-1=a3+an-2=鈥?ak+an-k+1锛宬鈭圢x
涓夈€佽嫢m锛宯锛宲锛宷鈭圢x锛屼笖m+n=p+q锛屽垯鏈塧m+an=ap+aq
鍥涖€佸浠绘剰鐨刱鈭圢x锛屾湁
Sk锛孲2k-Sk锛孲3k-S2k锛屸€︼紝Snk-S(n-1)k鈥︽垚绛夊樊鏁板垪銆?/p>
绛夋瘮鏁板垪
1.绛夋瘮涓」
濡傛灉鍦╝涓巄涓棿鎻掑叆涓€涓暟G锛屼娇a锛孏锛宐鎴愮瓑姣旀暟鍒楋紝閭ｄ箞G鍙仛a涓巄鐨勭瓑姣斾腑椤广€?/p>
鏈夊叧绯伙細
娉細涓や釜闈為浂鍚屽彿鐨勫疄鏁扮殑绛夋瘮涓」鏈変袱涓紝瀹冧滑浜掍负鐩稿弽鏁帮紝鎵€浠2=ab鏄痑,G,b涓夋暟鎴愮瓑姣旀暟鍒楃殑蹇呰涓嶅厖鍒嗘潯浠躲€?/p>
2.绛夋瘮鏁板垪閫氶」鍏紡
an=a1xq鈥?n-1)(鍏朵腑棣栭」鏄痑1锛屽叕姣旀槸q)
an=Sn-S(n-1)(n鈮?)
鍓峮椤瑰拰
褰搎鈮?鏃讹紝绛夋瘮鏁板垪鐨勫墠n椤瑰拰鐨勫叕寮忎负
Sn=a1(1-q鈥檔)/(1-q)=(a1-a1xq鈥檔)/(1-q)(q鈮?)
褰搎=1鏃讹紝绛夋瘮鏁板垪鐨勫墠n椤瑰拰鐨勫叕寮忎负
Sn=na1
3.绛夋瘮鏁板垪鍓峮椤瑰拰涓庨€氶」鐨勫叧绯?/p>
an=a1=s1(n=1)
an=sn-s(n-1)(n鈮?)
4.绛夋瘮鏁板垪鎬ц川
(1)鑻銆乶銆乸銆乹鈭圢x锛屼笖m+n=p+q锛屽垯am路an=ap路aq;
(2)鍦ㄧ瓑姣旀暟鍒椾腑锛屼緷娆℃瘡k椤逛箣鍜屼粛鎴愮瓑姣旀暟鍒椼€?/p>
(3)浠庣瓑姣旀暟鍒楃殑瀹氫箟銆侀€氶」鍏紡銆佸墠n椤瑰拰鍏紡鍙互鎺ㄥ嚭锛歛1路an=a2路an-1=a3路an-2=鈥?ak路an-k+1锛宬鈭坽1,2,鈥︼紝n}
(4)绛夋瘮涓」锛歲銆乺銆乸鎴愮瓑姣旀暟鍒楋紝鍒檃q路ap=ar2锛宎r鍒欎负ap锛宎q绛夋瘮涓」銆?/p>
璁跋€n=a1路a2鈥n锛屽垯鏈壪€2n-1=(an)2n-1锛屜€2n+1=(an+1)2n+1
鍙﹀锛屼竴涓悇椤瑰潎涓烘鏁扮殑绛夋瘮鏁板垪鍚勯」鍙栧悓搴曟寚鏁板箓鍚庢瀯鎴愪竴涓瓑宸暟鍒?鍙嶄箣锛屼互浠讳竴涓鏁癈涓哄簳锛岀敤涓€涓瓑宸暟鍒楃殑鍚勯」鍋氭寚鏁版瀯閫犲箓Can锛屽垯鏄瓑姣旀暟鍒椼€傚湪杩欎釜鎰忎箟涓嬶紝鎴戜滑璇达細涓€涓椤圭瓑姣旀暟鍒椾笌绛夊樊鏁板垪鏄€滃悓鏋勨€濈殑銆?/p>
(5)绛夋瘮鏁板垪鍓峮椤逛箣鍜孲n=a1(1-q鈥檔)/(1-q)
(6)浠绘剰涓ら」am锛宎n鐨勫叧绯讳负an=am路q鈥?n-m)
(7)鍦ㄧ瓑姣旀暟鍒椾腑锛岄椤筧1涓庡叕姣攓閮戒笉涓洪浂銆?/p>
娉ㄦ剰锛氫笂杩板叕寮忎腑a鈥檔琛ㄧずa鐨刵娆℃柟銆?/p>
鏁板涓夎褰㈡枩杈硅绠楀叕寮?/strong>
鏂滆竟鏄寚鐩磋涓夎褰腑鏈€闀跨殑閭ｆ潯杈癸紝涔熸寚涓嶆槸鏋勬垚鐩磋鐨勯偅鏉¤竟銆傚湪鍕捐偂瀹氱悊涓紝鏂滆竟绉颁綔鈥滃鸡鈥濄€?/p>
涓夎褰㈡枩杈归暱绛変簬鏍瑰彿涓嬩袱鐩磋杈圭殑骞虫柟鍜岋紝鍗虫枩杈筩=鈭?a^2+b^2)
瑙ｇ瓟杩囩▼濡備笅锛?/p>
(1)鍦ㄧ洿瑙掍笁瑙掑舰涓弧瓒冲嬀鑲″畾鐞嗏€斿湪骞抽潰涓婄殑涓€涓洿瑙掍笁瑙掑舰涓紝涓や釜鐩磋杈硅竟闀跨殑骞虫柟鍔犺捣鏉ョ瓑浜庢枩杈归暱鐨勫钩鏂广€傛暟瀛﹁〃杈惧紡锛歛虏+b虏=c虏
(2)a虏+b虏=c虏姹俢锛屽洜涓篶鏄竴鏉¤竟锛屾墍浠ュ氨鏄眰澶т簬0鐨勪竴涓牴銆傚嵆c=鈭?a虏+b虏)銆?/p>
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鎻愰珮鏁板鎴愮哗鐨勭獚闂ㄦ槸浠€涔?/strong>
鎵炬紡娲?/p>
瀛︾敓濡備綍鎵捐嚜宸卞绉戜笂鐨勬紡娲炲憿?涓昏灏辨槸瑕佸湪棰勪範 鏃舵壘婕忔礊銆備笂璇惧鐢熺殑瀛︿範鐩爣鏄庣‘锛屾敞鎰忓姏鎵嶄細闆嗕腑锛屽惉璇炬晥鐜囨墠浼氶珮銆傞櫎浜嗛涔狅紝鍋氶 涔熸槸涓€绉嶅緢濂界殑鎵炬紡娲炵殑鏂瑰紡銆?/p>
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涓嶈杞绘槗鏀捐繃涓€閬撻敊棰?/p>
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钀藉疄鐨勫叧閿槸妫€娴嬪拰閲嶅
钀藉疄灏辨槸纭亾鐞嗐€傜湅鑷繁琛ユ紡娲炵殑鏁堟灉濡備綍鏈€濂界殑鏂瑰紡灏辨槸妫€娴嬶紝澶氭妫€娴嬫病鏈夐棶棰樹簡锛岄偅涔堣繖涓紡娲炲氨涓嶄笂浜嗐€傝ˉ婕忔礊涔熶笉鏄竴娆°€佷袱娆″氨鑳借В鍐筹紝闇€瑕佷竴瀹氱殑閲嶅銆?/p>
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蹇呬慨浜旂浜岀珷鏁板鐭ヨ瘑鐐规€荤粨鐩稿叧鏂囩珷锛?/strong>
鈽?楂樹腑鏁板蹇呬慨浜岀煡璇嗙偣鎬荤粨
鈽?楂樹竴鏁板蹇呬慨浜旂煡璇嗙偣鎬荤粨褰掔撼
鈽?楂樹竴骞寸骇鏁板蹇呬慨浜旂煡璇嗙偣鏈€鏂板綊绾?021
鈽?鍏勾绾т笂鍐屼汉鏁欑増鏁板绗簩绔犵煡璇嗙偣褰掔撼鎬荤粨
鈽?楂樹簩鏁板閲嶇偣澶嶄範鐭ヨ瘑鐐瑰綊绾?绡?/a>
鈽?2021楂樹竴鏁板蹇呬慨浜旂煡璇嗙偣妗嗘灦
鈽?楂樹笁鏁板閲嶈鐭ヨ瘑鐐规€荤粨浜旂瘒
鈽?楂樹簩鏁板蹇呬慨浜旂煡璇嗙偣鎬荤粨褰掔撼浜旂瘒鍒嗕韩
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鈽?楂樹簩鏁板鐭ヨ瘑鐐归噸鐐规⒊鐞嗗綊绾?绡?/a>