1+2+3一直加到n化简等于什么？ 1+2+3+n怎么化简过程要写
1+2+3+\u4e00\u76f4\u52a0\u5230n\u600e\u4e48\u7b97\u5982\u679c\u4f60\u8bf4\u7684\u662f\u6570\u5b66\u95ee\u9898 \u90a3\u4e48\u5c31\u6709\u4e00\u4e2a\u516c\u5f0f \u524dn\u9879\u548c\u7b49\u4e8e \uff08n*(1+n)\uff09/2
\u5982\u679c\u4f60\u8bf4\u7684\u7f16\u7a0b\u95ee\u9898
\u4f60\u53ef\u4ee5\u4f7f\u7528\u4e2afor\u5faa\u73af
public class Test{
public static void main(String[] args){
Scanner sca = new Scanner(System.in);
int n = sca.nextInt();//\u8fd9\u53e5\u8bdd\u610f\u601d\u662f\u4f60\u4ece\u952e\u76d8\u8f93\u5165\u4e00\u4e2a\u6570\uff0c\u5982\uff1a\u4f60\u8f93\u7684\u662f10 \u90a3\u4e48n = 10
int sum = 0;
for(int i = 1;i<=n;i++){
sum = sum + i;
}
System.out.println(sum);
}
}
\u8f93\u51fa\u6765\u7684\u7ed3\u679csum \u5c31\u662f\u4f60\u60f3\u8981\u7684\u524dN\u9879\u7684\u548c
\u4f60\u53bb\u8bd5\u8bd5
1+2+...+n=n(1+n)/2
1+2+3+……+n＝（1+n）×n÷2文字助记法:首项+尾项×项数÷2
（1+n)n除2
(1+n)*n/2
n*（n+1)/2
二分之n平方加n
绛旓細鐢1+2+3+4+5+鈥︹+n=n(n+1)/2寰,灏唍鎹㈡垚n+1,灏唍+1鎹㈡垚n+2锛屽嵆1+2+3+4+5+...+n+(n+1)=(n+1)(n+2)/2
绛旓細杩囩▼濡備笅:璁1^3+2^3+...n^3=P(n)涓よ竟鍙栧鏁板緱 3(1^2+2^2+...+n^2)=P(n)鐨勫鏁 鐢变簬1^2+2^2+...+n^2=1/6n(n+1)(2n+1)鎵浠(n)鐨勫鏁=1/2n(n+1)(2n+1)=1/2(2n^3+3n^2+n)鍐嶅1/2(2n^3+3n^2+n)鍙栫Н鍒嗗緱1/4(n^4+2n^3+n^2)+C(C涓哄父鏁)鍖栫畝寰...
绛旓細鏈夊叕寮忥細1 + 2 + 3 + 鈥︹ + n = n(n+1)/2 锛屾墍浠 m = 3(1 + 2 + 3 + 鈥︹ + n) = 3n(n+1)/2 銆
绛旓細鍊掕繃鏉ュ啀鍔犱竴閬嶏紝鍐嵜2锛岀殑n锛n+1)/2 鍗1+ 2+ 3+ 4+ 5+鈥︹+n-4+n-3+n-2+n-1+n +n+n-1+n-2+n-3+n-4+鈥︹+5+ 4+ 3+ 2+ 1 涓婁笅瀵瑰簲锛屼笂涓嬬浉鍔犻兘绛変簬锛坣+1)锛屼竴鍏辨湁n涓紙n+1锛夋墍浠ュ叡n*锛坣+1锛夛紝鍥犱负鏄袱鍊嶏紝鎵浠*锛坣+1)/2 ...
绛旓細1璁 s=1+2+3+...+(n-1)鍒 s=(n-1)+(n-2)+...+1涓ゅ紡鐩稿姞 鏈 2s=n+n+...n (鍏眓-1 椤)鍒 s=(n*(n-1))/22璁緎=8+16+24+...8n鍒 s=8n+8*(n-1)+...+8涓ゅ紡鐩稿姞 鏈 2s=8(n+1)+8(n+1)+...+8(n+1) (鍏眓 椤)鍒 s=(n*8*(n+1))/2=4...
绛旓細鎬昏n-1椤癸紝1+2+3+鈥+(n鈥1)涓虹涓缁勬帓鍒楋紝鍐嶇敤涓缁勫弽鍚戞帓鍒楋紙n-1)+鈥+3+2+1.涓ょ粍鏁版嵁鎸夌収娆″簭鐩稿姞锛岄櫎浠2锛屽嵆涓哄叾涓涓缁勬帓鍒楃殑鍜屽硷細鍗1+锛坣-1锛+ 2+锛坣-2锛...+锛坣-1锛+1鐨勫奸櫎浠2锛屾诲叡鏈夛紙n-1锛変釜n鍦ㄤ竴璧凤紝鎵浠ユ湁n锛坣-1锛夛紝鍐嶉櫎浠2锛屽嵆涓簄(n -1)/2銆
绛旓細n^3-(n-1)^3=1*[n^2+(n-1)^2+n(n-1)]=n^2+(n-1)^2+n^2-n =2*n^2+(n-1)^2-n 2^3-1^3=2*2^2+1^2-2 3^3-2^3=2*3^2+2^2-3 4^3-3^3=2*4^2+3^2-4 ...n^3-(n-1)^3=2*n^2+(n-1)^2-n 鍚勭瓑寮忓叏鐩稿姞 n^3-1^3=2*(2^2+3^2+....
绛旓細1+2+3+...+锛n+1锛=锛1+n+1锛墄锛坣+1锛壝2 =锛坣+2锛夛紙n+1锛/2
绛旓細鍏堜护S锛1²+2²+3²+鈥+n²鍐嶅掕繃鏉锛漬²+(n锛1)²+鈥+2²+1²锛屽啀鐩稿姞闄や互2
绛旓細瑙ｏ細鍘熷紡=n+4銆愶紙1+n锛墄n梅2銆=n+2锛1+n锛塶 =2n²+3n 浜诧紝璇枫愰噰绾崇瓟妗堛戯紝鎮ㄧ殑閲囩撼鏄垜绛旈鐨勫姩鍔涳紝璋㈣阿銆
