计算自然数1至50的和 在自然数1至50中，将所有不能被3除尽的数相加，所得的和是（...
\u4ece1\u523050\u8fd950\u4e2a\u81ea\u7136\u6570\u4e2d\uff0c\u53d6\u4e24\u4e2a\u6570\u76f8\u52a0\uff0c\u8981\u4f7f\u5b83\u4eec\u7684\u548c\u5927\u4e8e50\uff0c\u5171\u6709______\u79cd\u4e0d\u540c\u7684\u53d6\u6cd5\u4ece1\u523050\u8fd950\u4e2a\u81ea\u7136\u6570\u4e2d\uff0c\u53d6\u4e24\u4e2a\u6570\u76f8\u52a0\uff0c\u8981\u4f7f\u5b83\u4eec\u7684\u548c\u5927\u4e8e50\uff0c\u5171\u6709 625\u79cd\u4e0d\u540c\u7684\u53d6\u6cd5\u3002
\u5206\u6790\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u5f53\u5176\u4e2d\u4e00\u4e2a\u6570\u662f50\u7684\u65f6\u5019\uff0c\u53e6\u4e00\u4e2a\u65701\u523049\u90fd\u53ef\u4ee5\uff0c\u670949\u79cd\u3002
\u5f53\u5176\u4e2d\u4e00\u4e2a\u6570\u662f49\u7684\u65f6\u5019\uff0c\u53e6\u5916\u4e00\u4e2a\u6570\u662f2\u523048\uff0c\u57282\u523048\u4e4b\u95f4\u670948-2+1=47\u4e2a\u6570\u3002
\u4ee5\u6b64\u7c7b\u63a8\u3002
49+47+45+43+\u2026+1
=\uff081+49\uff09\u00d725\u00f72
=25\u00d725\uff0c
=625\uff08\u79cd\uff09
\u7b54\uff1a\u4ece1\u523050\u8fd950\u4e2a\u81ea\u7136\u6570\u4e2d\uff0c\u53d6\u4e24\u4e2a\u6570\u76f8\u52a0\uff0c\u8981\u4f7f\u5b83\u4eec\u7684\u548c\u5927\u4e8e50\uff0c\u5171\u6709 625\u79cd\u4e0d\u540c\u7684\u53d6\u6cd5\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u52a0\u6cd5\u539f\u7406\u662f\u5206\u7c7b\u8ba1\u6570\u539f\u7406\uff0c\u5e38\u7528\u4e8e\u6392\u5217\u7ec4\u5408\u4e2d\uff0c\u5177\u4f53\u662f\u6307\uff1a\u505a\u4e00\u4ef6\u4e8b\u60c5\uff0c\u5b8c\u6210\u5b83\u6709n\u7c7b\u65b9\u5f0f\uff0c\u7b2c\u4e00\u7c7b\u65b9\u5f0f\u6709M1\u79cd\u65b9\u6cd5\uff0c\u7b2c\u4e8c\u7c7b\u65b9\u5f0f\u6709M2\u79cd\u65b9\u6cd5\uff0c\u2026\u2026\uff0c\u7b2cn\u7c7b\u65b9\u5f0f\u6709Mn\u79cd\u65b9\u6cd5\uff0c\u90a3\u4e48\u5b8c\u6210\u8fd9\u4ef6\u4e8b\u60c5\u5171\u6709M1+M2+\u2026\u2026+Mn\u79cd\u65b9\u6cd5\u3002
\u6bd4\u5982\u8bf4\uff1a\u4ece\u6b66\u6c49\u5230\u4e0a\u6d77\u6709\u4e58\u706b\u8f66\u3001\u98de\u673a\u3001\u8f6e\u82393\u79cd\u4ea4\u901a\u65b9\u5f0f\u53ef\u4f9b\u9009\u62e9\uff0c\u800c\u706b\u8f66\u3001\u98de\u673a\u3001\u8f6e\u8239\u5206\u522b\u6709k1\uff0ck2\uff0ck3\u4e2a\u73ed\u6b21\uff0c\u90a3\u4e48\u4ece\u6b66\u6c49\u5230\u4e0a\u6d77\u5171\u6709 k1+k2+k3\u79cd\u65b9\u5f0f\u53ef\u4ee5\u5230\u8fbe\u3002
\u6392\u5217\u7ec4\u5408\u8ba1\u7b97\u65b9\u6cd5\u5982\u4e0b\uff1a
\u6392\u5217A(n,m)=n\u00d7\uff08n-1\uff09.\uff08n-m+1\uff09=n!/\uff08n-m\uff09!(n\u4e3a\u4e0b\u6807,m\u4e3a\u4e0a\u6807,\u4ee5\u4e0b\u540c)
\u7ec4\u5408C(n,m)=P(n,m)/P(m,m) =n!/m!\uff08n-m\uff09!\uff1b
\u4f8b\u5982\uff1a
A(4,2)=4!/2!=4*3=12
C(4,2)=4!/(2!*2!)=4*3/(2*1)=6
\u601d\u8def\uff1a\u4ece1\u52a0\u523050\uff0c\u4e00\u5171\u662f1275
\u80fd\u88ab\u4e09\u9664\u5c3d\u7684\u6570\u4e3a\uff0c3\uff0c6\uff0c9\u2026\u2026\uff0c48\uff0c\u8fd9\u4e9b\u6570\u52a0\u8d77\u6765\u662f408
\u6240\u4ee5\u4e0d\u80fd\u88ab\u4e09\u6574\u9664\u7684\u6570\u7684\u548c\u662f1275-408=867
的公式：S=N*(N+1)/2
自然数1至50的和=51*50/2=1275
绛旓細49+47+45+43+鈥+1锛=锛1+49锛壝25梅2锛=25脳25锛=625锛堢锛夛紱绛旓細浠1鍒50杩50涓鑷劧鏁涓紝鍙栦袱涓暟鐩稿姞锛岃浣垮畠浠鐨勫拰澶т簬50锛屽叡鏈 625绉嶄笉鍚岀殑鍙栨硶锛涙晠绛旀涓猴細625锛
绛旓細1-50鐨鎵鏈鑷劧鏁涓紝鍗曟暟涓庡弻鏁板悇25涓傚彲浠ヤ袱涓ょ浉鍑忋傚崟鏁1銆3銆5鈥︹﹀弻鏁2銆4銆6銆8 (2+4+6+8鈥+50)-(1+3+5+鈥+49)=(2-1)+(4-3)+(6-5)+鈥︼紙50-49锛=1+1+1+鈥+1 =25 鎵鏈夊弻鏁鐨勫拰澶э紝澶25銆
绛旓細浠1鍒50杩50涓鑷劧鏁涓紝鍙栦袱涓暟鐩稿姞锛岃浣垮畠浠鐨勫拰澶т簬50锛屽叡鏈 625绉嶄笉鍚岀殑鍙栨硶銆傚垎鏋愯繃绋嬪涓嬶細褰撳叾涓竴涓暟鏄50鐨鏃跺欙紝鍙︿竴涓鏁1鍒49閮藉彲浠ワ紝鏈49绉嶃傚綋鍏朵腑涓涓暟鏄49鐨勬椂鍊欙紝鍙﹀涓涓暟鏄2鍒48锛屽湪2鍒48涔嬮棿鏈48-2+1=47涓暟銆備互姝ょ被鎺ㄣ49+47+45+43+鈥+1 =锛1+49锛壝25...
绛旓細1-100鎵鏈夋暟鍜=1+2+..+100=(1+100)*100/2=5050 鎵鏈夊伓鏁板拰=2+4+...+100=2(1+2+...+50)=2(1+50)*50/2=2550 鎵鏈夊鏁板拰=5050-2550=2500 鎵鏈夎川鏁板拰=2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83+89+97=1060 鎵鏈夊悎鏁板拰=5050-1-1060=...
绛旓細public class Test10 {public static void main(String[] args){int i,sum=0;for(i=1;i<=50;i++){ sum+=i++;}System.out.println("sum="+sum);}}
绛旓細(1+9)*9/2 绗竴涓暟鏄1,鏈鍚庝竴涓暟鏄9.鎵浠1+9銆1鍒9鎬诲叡鏈9涓暟 鎵浠ヤ箻浠9 鏈鍚庤繕瑕侀櫎浠2 寰楀嚭鐨勬暟灏辨槸杩炵画鑷劧鏁扮殑鍜 锛1+9锛*9/2 =10*9/2 =5*9 =45 鍐嶆潵涓涓緥瀛 1+2+3+4+5+6+鈥︹+98+99+100[浠1涓鐩磋繛缁姞鍒100鐨勫拰]锛1+100锛*100/2 =101*100/2 =101*50 ...
绛旓細include <stdio.h> unsigned long func(unsigned long a,unsigned long b){ unsigned long sum;for(sum=0;a<=b;++a)sum+=a;return sum;} int main(){ printf("%lu\n",func(1,50));printf("%lu\n",func(50,100));return 0;} ...
绛旓細1鏈1绉嶆儏鍐碉紝2鏈2绉嶆儏鍐碉紝3鏈3绉嶆儏鍐碘︹25鏈25绉嶆儏鍐 閬垮厤閲嶅锛26鏈24绉嶆儏鍐碉紝27鏈23绉嶆儏鍐碘︹49鏈1绉嶆儏鍐碉紝50鏈0绉嶆儏鍐 鏁呭叡鏈1+2+...+25+24+...+1=25x25=625绉嶈В娉
绛旓細鍦1~50鐨勮嚜鐒舵暟涓紝姣忔鍙栦袱涓笉鍚岀殑鑷劧鏁扮浉鍔狅紝鍏辨湁50*49/2=1225绉 鍏朵腑缁撴灉绛変簬51鐨勬湁25绉嶏紝澶т簬51鐨勫拰灏忎簬51鐨勭浉鍚=(1225-25)/2=600 鈭村拰澶т簬50鐨勫叡鏈600+25=625绉
