求数列1、3、6、10、15、21……的通项公式 1.3.6.10.15.21…是数列吗？通项公式是什么？谢谢
\u6570\u52171\uff0c3\uff0c6\uff0c10\uff0c15\u2026\u7684\u4e00\u4e2a\u901a\u9879\u516c\u5f0f\u4e3a______n(n+1)/2\u3002
\u4ed4\u7ec6\u89c2\u5bdf\u6570\u52171\uff0c3\uff0c6\uff0c10\uff0c15\u2026\u53ef\u4ee5\u53d1\u73b0\uff1a
\uff081\uff091=1
\uff082\uff093=1+2
\uff083\uff096=1+2+3
\uff084\uff0910=1+2+3+4
\uff085\uff0915=1+2+3+4+5
\u2026\u2026
\uff086\uff09\u7b2cn\u9879\u4e3a\uff1a1+2+3+4+\u2026+n= n(n+1)/2\u3002\uff081\u30012\u30013\u30014\u30015\u2026\u2026n\uff0c\u662f\u4e00\u4e2a\u4ee51\u4e3a\u9996\u9879\uff0c1\u4e3a\u516c\u5dee\u7684\u7b49\u5dee\u6570\u5217\uff0c\u7b2cn\u9879\u5c31\u662f\u5bf9\u5176\u6c42\u548c\uff09
\u6269\u5c55\u8d44\u6599\uff1a
\u7b49\u5dee\u6570\u5217\u7684\u5176\u4ed6\u63a8\u8bba\uff1a
\u2460\u548c=\uff08\u9996\u9879+\u672b\u9879\uff09\u00d7\u9879\u6570\u00f72\u3002
\u2461\u9879\u6570=\uff08\u672b\u9879-\u9996\u9879\uff09\u00f7\u516c\u5dee+1\u3002
\u2462\u9996\u9879=2x\u548c\u00f7\u9879\u6570-\u672b\u9879\u6216\u672b\u9879-\u516c\u5dee\u00d7\uff08\u9879\u6570-1\uff09\u3002
\u2463\u672b\u9879=2x\u548c\u00f7\u9879\u6570-\u9996\u9879\u3002
\u2464\u672b\u9879=\u9996\u9879+\uff08\u9879\u6570-1\uff09\u00d7\u516c\u5dee\u3002
\u901a\u9879\u516c\u5f0f\u6c42\u6cd5\u793a\u4f8b\uff1a
{an}\u6ee1\u8db3a₁+ 2a₂+ 3a₃+\u2026\u2026+ n\u00d7an = n(n+1)(n+2)
\u89e3\uff1a\u4ee4bn = a₁+ 2a₂+ 3a₃+\u2026\u2026+ n\u00d7an = n(n+1)(n+2)
n\u00d7an = bn - bn-1 = n(n+1)(n+2)-(n-1)n(n+1)
\u2234an = 3\uff08n+1\uff09
\u662f\u6570\u5217\u3002
\u901a\u9879\u516c\u5f0f\u662f \uff08n²+n\uff09/2\u3002
a\uff081\uff09=1\u00d7\uff081+1\uff09\u00f72=1\uff1b
a\uff082\uff09=2\u00d7\uff082+1\uff09\u00f72=3\uff1b
a\uff083\uff09=3\u00d7\uff083+1\uff09\u00f72=6\uff1b
a\uff084\uff09=4\u00d7\uff084+1\uff09\u00f72=10\uff1b
a\uff085\uff09=5\u00d7\uff085+1\uff09\u00f72=15\uff1b
a\uff086\uff09=6\u00d7\uff086+1\uff09\u00f72=21\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u2460\u6570\u5217\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u51fd\u6570\u3002\u5176\u7279\u6b8a\u6027\u4e3b\u8981\u8868\u73b0\u5728\u5176\u5b9a\u4e49\u57df\u548c\u503c\u57df\u4e0a\u3002\u6570\u5217\u53ef\u4ee5\u770b\u4f5c\u4e00\u4e2a\u5b9a\u4e49\u57df\u4e3a\u6b63\u6574\u6570\u96c6N*\u6216\u5176\u6709\u9650\u5b50\u96c6{1\uff0c2\uff0c3\uff0c\u2026\uff0cn}\u7684\u51fd\u6570\uff0c\u5176\u4e2d\u7684{1\uff0c2\uff0c3\uff0c\u2026\uff0cn}\u4e0d\u80fd\u7701\u7565\u3002
\u2461\u7528\u51fd\u6570\u7684\u89c2\u70b9\u8ba4\u8bc6\u6570\u5217\u662f\u91cd\u8981\u7684\u601d\u60f3\u65b9\u6cd5\uff0c\u4e00\u822c\u60c5\u51b5\u4e0b\u51fd\u6570\u6709\u4e09\u79cd\u8868\u793a\u65b9\u6cd5\uff0c\u6570\u5217\u4e5f\u4e0d\u4f8b\u5916\uff0c\u901a\u5e38\u4e5f\u6709\u4e09\u79cd\u8868\u793a\u65b9\u6cd5\uff1aa.\u5217\u8868\u6cd5\uff1bb\u3002\u56fe\u50cf\u6cd5\uff1bc.\u89e3\u6790\u6cd5\u3002\u5176\u4e2d\u89e3\u6790\u6cd5\u5305\u62ec\u4ee5\u901a\u9879\u516c\u5f0f\u7ed9\u51fa\u6570\u5217\u548c\u4ee5\u9012\u63a8\u516c\u5f0f\u7ed9\u51fa\u6570\u5217\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u6570\u5217
an=n(n+1)/2
an-n(n+1)/2
绛旓細鏁板垪1,3,6,10,15,21锛鐨勯氶」鍏紡涓篴n = (n^2 + n) / 2銆傝繖涓暟鍒楃殑閫氶」鍏紡鍙互閫氳繃鏁板褰掔撼娉曟潵姹傝В銆傞鍏堬紝鎴戜滑鍙互鍐欏嚭鏁板垪鐨勫墠鍑犻」锛氱1椤癸細1 绗2椤癸細1 + 2 = 3 绗3椤癸細1 + 2 + 3 = 6 绗4椤癸細1 + 2 + 3 + 4 = 10 绗5椤癸細1 + 2 + 3 + 4 + 5 = 15 绗...
绛旓細浠旂粏瑙傚療鏁板垪1锛3锛6锛10锛15鈥﹀彲浠ュ彂鐜帮細锛1锛1=1 锛2锛3=1+2 锛3锛6=1+2+3 锛4锛10=1+2+3+4 锛5锛15=1+2+3+4+5 鈥︹︼紙6锛夌n椤逛负锛1+2+3+4+鈥+n= n(n+1)/2銆傦紙1銆2銆3銆4銆5鈥︹锛屾槸涓涓互1涓洪椤癸紝1涓哄叕宸殑绛夊樊鏁板垪锛岀n椤瑰氨鏄鍏舵眰鍜岋級...
绛旓細浠旂粏瑙傚療鏁板垪1锛3锛6锛10锛15鈥﹀彲浠ュ彂鐜帮細锛1锛1=1 锛2锛3=1+2 锛3锛6=1+2+3 锛4锛10=1+2+3+4 锛5锛15=1+2+3+4+5 鈥︹︼紙6锛夌n椤逛负锛1+2+3+4+鈥+n= n(n+1)/2銆傦紙1銆2銆3銆4銆5鈥︹锛屾槸涓涓互1涓洪椤癸紝1涓哄叕宸殑绛夊樊鏁板垪锛岀n椤瑰氨鏄鍏舵眰鍜岋級...
绛旓細1銆侀氶」鍏紡涓簄(n+1)/2銆備粩缁嗚瀵熸暟鍒1锛3锛6锛10锛15鈥﹀彲浠ュ彂鐜帮細锛1锛1=1 锛2锛3=1+2 锛3锛6=1+2+3 锛4锛10=1+2+3+4 锛5锛15=1+2+3+4+5 鈥︹︼紙6锛夌n椤逛负锛1+2+3+4+鈥+n= n(n+1)/2銆傦紙1銆2銆3銆4銆5鈥︹锛屾槸涓涓互1涓洪椤癸紝1涓哄叕宸殑绛夊樊鏁板垪锛岀...
绛旓細鐢变笂闈㈠嚑涓鏁板垪鐨勯」鏈変笅闈㈢殑鍏紡:an-a(n-1)=n.閭ｄ箞渚濇鎶妌鍑1鏈:a(n-1)-a(n-2)=n-1 a(n-2)-a(n-3)=n-2 篓篓篓a2-a1=2 a1*1鎶婁笂寮忕浉鍔犳湁:an=1+2+3+鈥︹+n=n*(n+1)/2
绛旓細(1+n)n/2 鍥犱负锛1=1 3=1+2 6=1+2+3 10=1+2+3+4 ```绗琻椤逛负1+2+3+4+```+n 鍙傝冭祫鏂欙細baidu
绛旓細1銆3銆6銆10銆15銆21鐨勮寰嬫槸锛歛n-a(n-1)=n閫氶」鏄痑n=1+2+...+n=n*(n+1)/2銆傚鏋鏁板垪{an}鐨勭n椤筧n涓巒涔嬮棿鐨勫叧绯诲彲浠ョ敤涓涓叕寮忔潵琛ㄧず锛岃繖涓叕寮忓彨鍋氭暟鍒楃殑閫氶」鍏紡銆傛湁鐨勬暟鍒楃殑閫氶」鍙互鐢ㄤ袱涓垨涓や釜浠ヤ笂鐨勫紡瀛愭潵琛ㄧず銆傛病鏈夐氶」鍏紡鐨勬暟鍒椾篃鏄瓨鍦ㄧ殑锛屽鎵鏈夎川鏁扮粍鎴愮殑鏁板垪銆傛暟鍒椾篃...
绛旓細鏁板棰樻壘瑙勫緥锛1锛3锛6锛10锛15鐨勮寰嬫槸3姣1澶2锛6姣3澶3锛10姣6澶4锛5姣10澶5锛屼篃灏辨槸璇达紝1+2=3锛3+3=6锛6+4=10锛10+5=15銆傚氨鏄鍚庝竴浣嶆暟姣斿墠涓浣嶆暟渚濇澶1銆
绛旓細3 6 10 15 绗涓灞傦細Y1 2 3 4 5 绗竴灞傦細Y2 1 1 1 绗竴灞傦細Y3 鐪嬪嚭鏉ヨ寰嬫病鏈 涓婇潰涓や釜鏁扮浉鍑忓緱鍒颁笅闈㈢殑鏁帮紝鍏卞噺涓ゅ眰灏辨槸鐩哥瓑浜 瀵逛簬杩欑褰技鐨鏁板垪锛鏈変竴涓寰嬨傛垜浠Y1锛坣锛=b*n^2+c*n+d 閭ｄ箞鏈塝2(n)=Y1锛坣+1)-Y1锛坣)Y3(n)=Y2锛坣+1)-Y2锛坣)=甯告暟 鍒╃敤涓婇潰鐨...
绛旓細3-1=2 6-3=3 10-6=4 15-10=5 鐩搁偦涓ら」鐨勫樊鏋勬垚棣栭」涓2銆佸叕宸负1鐨勭瓑宸鏁板垪銆俛n-a1=(2+2+((n-1)-1)*1)*(n-1)/2 an=a1+2n-2+(n-1)(n-2)/2 =1+2n-2+(n²-3n+2)/2 =n²/2+n/2 閫氶」鍏紡锛 an=n²/2+n/2 ...
