Transcription of 第 9 章 無窮級數 (Infinite Series)
{{id}} {{{paragraph}}}
Example: confidence
第 9 章 無窮級數 (Infinite Series)
9 (Infinite series ) .. Taylor Taylor .. (Sequences) (sequence) N f, f(n) an fa1, a2, a3, ..g fang fang1n=1 a1 (first term),an n [ ] (1)an=pn,fang=f1,p2,p3, .. ,pn, ..g (2)bn= ( 1)n+11n,fbng=f1, 12,13, 14, ..g (3)cn=n 1n,fcng=f0,12,23,34, .. ,n 1n, ..g 89 9 (4)dn= ( 1)n+1,fdng=f1, 1,1, 1, .. ,( 1)n+1, ..g , , , (recursion formula) (1)a1= 1,an=an 1+ 1 (2)a1= 1,an=nan 1 (3) :x0= 1,xn+1=xn (sinxn x2ncosxn 2xn) sinx x2= 0 (4)Fibonacci :a1= 1,a2= 1,an+1=an+an 1 (1) fang 8 >0,9N n > N jan Lj< , fang (limit) L limn!1an=L n!1,an!L (2) , (converge), (diverge) (3) fang M, N, 8n > N)an> M, fang (diverges to infinity) limn!1an=1, an!
第9 章無窮級數 9.1 數列 (4) 若an ‚ an+1,8n, 則稱fang 為非上升數列 (nondecreasing sequence)。 (5) fang 為上升或下降數列, 則統稱為單調 (monotonic)。 (6) 若存在 N, 使得 an < an+1,8 n > N, 則稱fang 為終極上升 (ultimately increasing) 數列 定義 9.1.19. (1) 若存在 M, 使得 an • M,8n, 則稱fang 為有上界 (bounded above), 且 M
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: