高一数学数列问题，请问数学学霸此题怎么做？求学霸赐教 求数学学霸,高一数学题,画图题,数学学渣拜托学霸了
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a(n-1)-a(n-2)=2(n-1)-1
......
a2-a1=2x2-1
把以上等式两边分别相加得
a(n)-a1=2[n+(n-1)+(n-2)+......+2]-(n-1)
=n(n-1)-2-(n-1)
=(n-1)²-2
绛旓細褰搉>=5鏃讹紝2^n+n>2^n锛屽洜姝n<1/2^n锛屽n浠5寮濮嬫眰鍜屼笉浼氳秴杩1/32+1/64+...=1/32/(1-1/2)=1/16<1/5锛屽洜姝ゅ墠n椤瑰拰Tn<1/3+1/6+1/11+1/20+1/5=37/44
绛旓細璁炬暟鍒椾负{an} 7=3脳3-2 19=7脳3-2 55=19脳3-2 163=55脳3-2 瑙勫緥锛氫粠绗2椤瑰紑濮嬶紝姣忎竴椤归兘绛変簬瀹冨墠闈竴椤圭殑3鍊嶏紝鍐嶅噺2銆俷鈮2鏃讹紝an=3a(n-1)-2 an -1=3a(n-1)-3=3[a(n-1)-1](an -1)/[a(n-1)-1]=3锛屼负瀹氬 a1-1=3-1=2锛屾暟鍒{an -1}鏄互2涓洪椤癸紝3涓...
绛旓細鍒╃敤绛夊樊鏁板垪鍏紡锛屼唬鍏3锛宎5锛屽彲瑙ｅ嚭a1=1锛宒=2锛岄氶」=1+2锛坣-1锛=2n-1 瀵圭浜屽紡澶勭悊銆傚垎瀛愮涓椤=2n-3锛岀浜岄」=2n-1锛屽彉鎹㈡垚宸殑褰㈠紡=锛-1/锛2n-1锛+1/锛2n-3锛夛級鍒楀嚭bn锛屽彲浠ョ湅鍑猴紝sn=-1-1/锛2n-1锛=锛-2n锛/锛2n-1锛
绛旓細绛夊樊鏁板垪鐨勯氶」鍏紡涓猴細鍏朵腑a1涓烘暟鍒楃殑棣栭」锛宒涓哄叕宸備唬鍏3=9锛宎9=12锛屽垯锛氳В鏂圭▼绁栵紝寰楋細a1=8锛宒=0.5銆傜瓑宸暟鍒楀墠n椤瑰拰鍏紡涓猴細鎸夌収绗竴涓叕寮忥細S12=12脳8+12脳锛12-1锛壝0.5/2=96+33=129銆傛寜鐓х浜屼釜鍏紡锛歛12=8+锛12-1锛壝0.5=13.5銆係12=12脳锛8+13.5锛/2=129銆
绛旓細鍥炵瓟锛氱敱宸茬煡鍙緱浠庝笂鍒颁笅姣忓眰鐨勭摝鐗囨暟鏄互20涓洪椤瑰叕宸负1鐨勭瓑宸鏁板垪 a1=20 an=a1+(n-1)d=20+n-1=19+n a21=19+21=40 S21=21(a1+a21)/2=21(20+40)/2=630 涓鍏遍摵浜630鍧
绛旓細瑙ｇ瓟濡備笅锛歛n涓轰簡濂藉尯鍒嗭紝涓嬮潰閮藉啓鎴怉n 锛1锛夈佸洜涓篠n=n锛圓n+1锛-n²鎵浠锛坣-1锛=锛坣-1锛塠A锛坣-1锛+1]-锛坣-1锛²涓婇潰涓や釜寮忓瓙浣滃樊鍙緱 An=Sn-S锛坣-1锛=[n锛圓n+1锛-n²]-锛坣-1锛塠A锛坣-1锛+1]+锛坣-1锛²绠鍖栧緱An-A(n-1)=2 鍒橝2-A1=2 A3-...
绛旓細锛坣+3锛塧锛坣+1锛²-nan²+3a锛坣+1锛塧n=0 =[锛坣+3锛塧锛坣+1锛-nan]*[a锛坣+1锛+an] =0 鎵浠ワ細锛坣+3锛塧锛坣+1锛-nan = 0 a锛坣+1锛/ an = n/ (n+3)an/ a1 = 6 /n锛坣+1锛夛紙n+2锛塧n=2 /n锛坣+1锛夛紙n+2锛
绛旓細鍥炵瓟锛氭妸an-1-an-2=1/(2n-4)-1/(2n)鍐欏嚭鏉ヨ瘯璇(澶氬啓鍑犱釜绛夊紡鎬绘病閿),an-a1=1/2+1/4-1/2n-1/(2n+2),浠呬緵鍙傝,涓嶄竴瀹氬,鍛靛懙
绛旓細鏂规硶涓锛氾紙鏁板褰掔撼娉曪紝澶畝鍗...鑷繁鍋氾級鏂规硶浜岋細锛堟瀯閫鏁板垪锛夋牴鎹凡鐭ワ細1/an=1/a(n-1) +1/2 鎵浠1/an}鏄叕宸负1/2鐨勭瓑宸暟鍒 1/an=1/a1+(n-1)* 1/2=(n+1)/2 鎵浠n=2/(n+1)
绛旓細鍏堟妸杩欎釜鏁板垪鐨勫叕宸眰鍑烘潵锛岀劧鍚庢眰绗竷椤癸紝鏈鍚庣敤2闄や竴涓 骞朵笉闅撅紝鏈涢噰绾筹紒
