infi2HW06 - ∞ n =1 a 2 n mixehd ik oezp (!hlgend jxrd z`...

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6 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2008 x`exatl 28 :dybd jix`z A 4 lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz sca jxev oi` .oeilib xtqne ,f"z ,zeny xexiaa oiivl `p .wcedn yibdl `p .mixqlw e` zeiwy `ll .xry 1 libxz .mixehd ly zeqpkzd ewca n =3 1 n log n (log log n ) 2 .1 n =1 2 · 4 · 6 ··· 2 n 1 · 3 · 5 ··· (2 n +1) .2 n =2 1 (log n ) log n .3 n =1 n - n +1 n .4 n =1 sin( 1 n ) n .5 n =1 1 n ( n n - 1) .6 n =1 (1 - cos( π n )) .7 2 libxz :egiked . f 0 (0) 6 = 0 oke f (0) = 0 :miiwzn .qt`a dxifbe [ - 1 , 1] lr zxcben f ( x ) .xcazn n =1 f ( 1 n ) .1 .qpkzn n =1 f ( 1 n 2 ) .2 3 libxz qpkzn n =1 a n :miiwzn n =1 a n iaeig xeh lkl m` ogea zxciq z`xwip { γ n } n =1 ziaeig dxcq :mi`ad mialyd t"r ogea zxcq zniiw `ly egiked . lim n →∞ γ n a n = 0 m` wxe m` .dneqg zeidl dleki dpi` ogea zxcqy egiked .1 n =1 a n qpkzn xeh dzxfra epae γ n k k 2 zniiwnd γ n k dxcq zz zniiw dnl exiaqd .2 .ogea zxcq zniiw `ly okl ewiqde lim n →∞ γ n a n 6 = 0 exear xy` 1
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4 libxz :mikxc ipya qpkzn n =1 a n b n xehdy egiked .miqpkzn n =1 b 2 n - e
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Unformatted text preview: ∞ n =1 a 2 n mixehd ik oezp (!hlgend jxrd z` jynda wexfl xyt` dnl xiaqdl gekyl `l) | a n b n | ≤ a 2 n + b 2 n 2 .` :mixehl uxeey-iyew oeieeiy i` z` egiked .a ∞ X n =1 | a n b n | ≤ v u u t ∞ X n =1 a 2 n v u u t ∞ X n =1 b 2 n 5 libxz :xcazn `ad xehdy egiked ∞ X n =1 (-1) [ √ n ] √ n .oezgzd mlyd jxrd df [ · ] xy`k ? N 2 + N- l N 2 oia mekqd lr xnel elkez dn :fnx 6 libxz :egiked . S n = ∑ n k =1 f ( k ) oke I n = R n 1 f ( x ) dx :onqp . [1 , ∞ ) lr zcxei zipehepen f ( x ) ≥ .1 .zqpkzn u n = S n-I n .qpkzn 1 + 1 2 + 1 3 + ··· + 1 n-log n ik e`xd .2 elkez m`d .xlie` ly reawd `xwpe γ = 0 . 577215 ...- a oneqn efd dxcqd ly leabd :dxrd d`nn xzei xak dgezt dl`y `id ef dl`y ;dgica oaenk ef) ?ilpeivx epi` `ed ik gikedl .(dpy 2...
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This note was uploaded on 06/27/2008 for the course MATH Infi 2 taught by Professor Benyamini during the Winter '08 term at Technion.

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infi2HW06 - ∞ n =1 a 2 n mixehd ik oezp (!hlgend jxrd z`...

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