根据杨辉三角,请计算(x-1/x)的12次方的展开式中四次项的系数是？ (x+1+1/x)^4展开式中含X^2项的系数是?[有追加分...
\uff08x+1/x-2\uff09\u76844\u6b21\u65b9\u7684\u5c55\u5f00\u5f0f\u4e2dx\u7684\u5e73\u65b9\u7684\u7cfb\u6570\uff1f\u6839\u636e\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u542b x^2 \u9879\u7684\u7cfb\u6570\u4e3a C(5\uff0c2) (-2)^3 = - 80 \u3002
\u8fd9\u4e2a\u9898\u76ee\u662f\u521d\u4e2d\u9898\u76ee\u7684\u8bdd\uff0c\u90a3\u4e48\u628a
x
+
1/x
\u7ec4\u5408\u5728\u4e00\u8d77\uff0c\u76f4\u63a5\u5c55\u5f00\u3002
(a+b)^n
\u7684\u5c55\u5f00\u7cfb\u6570
\u53ef\u7528
\u201c
\u6768\u8f89\u4e09\u89d2\u201d\uff0c\u5982\u4e0b\u56fe\uff1a
1
1
1
2
1
1
3
3
1
1
4
6
4
1
\u4f59\u6b64\u7c7b\u63a8
\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d
(x
+
1
+
1/x)^4
=
[(x
+
1/x)
+
1]^4
=
(x
+
1/x)^4
+
4(x
+
1/x)^3
+
6(x
+
1/x)^2
+
4
(x
+
1/x)
+
1
(x
+
1/x)^4
\u5c55\u5f00\u5f0f\u7b2c2\u9879\u662f
x^3
*
1/x\uff0c\u5373
x^2\u9879\uff0c\u7cfb\u6570\u4e3a
4
(x
+
1/x)^3
\u5c55\u5f00\u5f0f\u4e2d\u65e0
x^2
\u9879
(x
+
1/x)^2
\u5c55\u5f00\u5f0f\u4e2d\uff0c\u7b2c\u4e00\u9879\u4e3a
x^2
\u9879\uff0c\u7cfb\u6570\u4e3a
1
\u56e0\u6b64
(x+1+1/x)^4\u5c55\u5f00\u5f0f\u4e2d\u542bX^2\u9879\u7684\u7cfb\u6570\u662f
4
+
6\u00d71
=
10
＝495x^4，
所以系数是 495。
绛旓細鍥涙椤规槸 C(12锛8)x^8(-1/x)^4 锛495x^4锛屾墍浠ョ郴鏁版槸 495銆
绛旓細瑙ｏ細(1)鏍规嵁浜岄」寮忕郴鏁扮殑鈥鏉ㄨ緣涓夎褰⑩濆彲鐭ワ細涓娆℃柟鐨勭郴鏁板拰鏄1+1锛2锛涗簩娆℃柟鐨勭郴鏁板拰鏄1+2+1锛4锛涗笁娆℃柟鐨勭郴鏁板拰鏄1+3+3+1锛8锛涒︹娆℃柟鐨勭郴鏁板拰鏄2^n銆備粠棰樼洰涓殑绯绘暟鍜屾槸64鍙煡锛宯=6銆傦紙濡傛灉鏈夌闉嬫彁鍑哄簲鑰冭檻绯绘暟鐨勬璐熷彿锛屽垯鎵鏈夋鏂圭殑绯绘暟鍜岄兘鏄0锛岃棰樻病娉曞仛锛(2)鐢璁＄畻鍙煡...
绛旓細a^5+5a^4+10a^3+10a^2+5a+1=(a+1)^5 杩欐槸鏉ㄨ緣涓夎鍨嬪晩 鎵浠 (x-1)^5+5(x-1)^4+10(x-1)^3+10(x-1)^2+5(x-1)= (x-1)^5+5(x-1)^4+10(x-1)^3+10(x-1)^2+5(x-1)+1-1= (x-1+1)^5-1 =x^5-1 ...
绛旓細1 1 1 1 2 1 1 3 3 1 鈥︹︽瘡涓涓暟锛堝嚭鏈宸﹁竟鍜屾渶鍙宠竟澶栵級閮芥槸涓婇潰涓や釜鏁扮殑鍜岋紝涔熷氨鏄褰撳墠鍧愭爣涓簒锛寉 閭ｄ箞a[x,y]:=a[x-1,y]+a[x-1,y-1]绠渚挎柟娉曟湁鏄湁锛屽氨鏄敤缁勫悎C鍙互绠楀嚭鏉ュ湪绗瑇琛岋紝y鍒楃殑鏁般備絾鏄湅LZ鐨勭▼搴忔槸璁＄畻绗琻琛岀殑鎵鏈夊肩殑鍜宮od 2009 鐨勪綑鏁帮紝鎵浠ヨ繕鏄敤...
绛旓細杩欐槸鏉ㄨ緣涓夎锛氫唬鐮佸涓嬶細include <stdio.h> include <stdlib.h> const int length = 10; // 瀹氫箟鏉ㄨ緣涓夎鐨勫ぇ灏 int main(void){ int nums[length][length];int i, j;/*璁＄畻鏉ㄨ緣涓夎*/ for(i=0; i<length; i++) { nums[i][0] = 1;nums[i][i] = 1;for(j=1; j<i; ...
绛旓細鏉ㄨ緣涓夎褰㈢殑瑙勫緥 1銆佹潹杈変笁瑙掑乏鍙充袱渚х殑鏁板瓧閮芥槸1锛鑰岄噷闈㈢殑鏁板瓧绛変簬瀹冭偐涓婄殑涓ゆ暟涔嬪拰銆2銆佺n琛岀殑鏁版墍缁勬垚鐨勬暟瀛椾负11n-1銆3銆佺n琛岀殑鏁板瓧涔嬪拰鏄2n-1銆4銆佹瘡涓鏂滅嚎涓婄殑鏁板瓧涔嬪拰绛変簬鎷愯澶勭殑鏁板瓧銆5銆佹瘡涓鏂滆鐨勬暟瀛楃浉鍔狅紝缁勬垚涓涓枑娉㈤偅濂戞暟鍒椼6銆佹瘡涓琛岀殑鏁板瓧鍒嗗埆鏄紙a+b锛塶杩欎竴澶氶」寮...
绛旓細鏉ㄨ緣涓夎鍏锋湁宸﹀彸瀵圭О鎬э紝鍗崇n琛岀殑绗琸涓暟瀛楃瓑浜庣n琛岀殑绗琻-k涓暟瀛椼傝繖涓绉版у彲浠ヤ娇寰璁＄畻鏉ㄨ緣涓夎鐨勬煇浜涢儴鍒嗘洿鍔犻珮鏁堛傛枩瀵硅瑙勫緥锛氫粠绗2琛屽紑濮嬶紝姣忔潯鏂滃瑙掔嚎涓婄殑鏁板瓧涔嬪拰閮芥槸2鐨勫箓銆備緥濡傦紝绗1涓枩瀵硅绾夸笂鐨勬暟瀛椾箣鍜屼负2^0=1锛绗2涓枩瀵硅绾夸笂鐨勬暟瀛椾箣鍜屼负2^1=2锛岀3涓枩瀵硅绾夸笂鐨...
绛旓細鈥鏉ㄨ緣涓夎鈥濈殑瑙勫緥鍏紡锛1銆佹瘡涓暟绛変簬瀹冧笂鏂逛袱鏁颁箣鍜屻2銆佹瘡琛屾暟瀛楀乏鍙冲绉帮紝鐢1寮濮嬮愭笎鍙樺ぇ銆3銆佺n琛岀殑鏁板瓧鏈塶锛1椤广4銆佺n琛屾暟瀛楀拰涓2锛撅紙n-1锛夛紙2鐨勶紙n-1锛夋鏂癸級銆5銆侊紙a锛媌锛夛季n鐨勫睍寮寮忎腑鐨勫悇椤圭郴鏁颁緷娆″搴旀潹杈変笁瑙掔殑绗紙n锛1锛夎涓殑姣忎竴椤广6銆佺n琛岀殑绗琺涓暟鍜岀n-...
绛旓細浠庤寰嬩腑鎴戜滑鍙互鐪嬪嚭鏉ㄨ緣涓夎褰㈡槸瀵圭О鐨勶紝瀹冩槸浜岄」寮忕郴鏁板湪涓夎褰腑鐨勪竴绉嶅嚑浣曟帓鍒椼傛潹杈変笁瑙掍腑n琛屼腑鐨勭i涓暟鏄痠-1涓墠n-1涓暟涔嬪拰锛屽嵆绗琻琛岀殑鏁板垎鍒负锛锛1)涓n琛屼箣鍓嶇殑鏁板瓧涔嬪拰銆傦紙2)涓n琛屼箣鍓嶇殑鏁板瓧涔嬪拰銆傦紙3)涓n琛屼箣鍓嶇殑鏁板瓧涔嬪拰銆傦紙4)涓n琛屼箣鍓嶇殑鏁板瓧涔嬪拰銆傚簲鐢 涓庢潹杈...
绛旓細鏉ㄨ緣涓夎鐨勫叕寮忥細姣忎竴琛岀殑鏁板瓧鏄笂涓琛岀浉閭讳袱涓暟瀛楃殑鍜屻傚叿浣撴潵璇达紝绗琻琛岀殑棣栧熬鏁板瓧閮芥槸1锛鍏朵綑鏁板瓧鍒欐槸涓婁竴琛岀浉閭讳袱涓暟瀛楃殑鍜屻備緥濡傦紝绗笁琛岀殑鏁板瓧涓虹2琛岀浉閭绘暟瀛楃殑鍜屻傚熀浜庤繖绉嶈寰锛屾潹杈変笁瑙鍙互缁х画鏃犻檺寤朵几涓嬪幓銆傚湪璁＄畻鏈虹瀛︿腑锛岃繖涓妯″紡涔熷彲浠ョ敤浜庢瀯閫犱竴绉嶅姩鎬佽鍒掔殑鏂规硶鏉ヨ绠椾换鎰忎綅缃殑鏁板...
