Infi2HW07 - 4 libxz `ede reaix `ed 4 oky F a epi` 12,lynl.mze` wlgn epi` reaixy mixtqnd lk zveaw F idz:xcazn `ad xehdy egiked F = f 1,f 2 onqp 12

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7 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2008 uxnl 6 :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 :qpkzn `ad xehd mxear α,β lk e`vn .1 X n =1 ( - 1) n - 1 ± α - ( n - β ) n n n :qpkzn `ad xehd iraih k lkl ik egiked .qt`l zt`ey zipehepene ziaeig a n .2 X n =1 ( - 1) b n k c a n 2 libxz ly iteq xtqnl hxt σ ( n ) = n m` iteq qetihn z`xwp (lre r"gg divwpet) σ : N N divhenxt qetihn divhenxt zgz a σ ( n ) xehd mekq edn . A enekqe i`pza qpkzn xeh a n idi .mi- n ?iteq qetihn dpi`y divhenxt i"r mekq eze` z` lawl xyt` m`d ?iteq 3 libxz :miiwzn a > 1 xear ik mixeh zeltkn i"r egiked ˆ X n =0 1 a n ! 2 = X n =0 n + 1 a n .ipnid xehd mekq z` aygl zpn lr jka eynzyde
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Unformatted text preview: 4 libxz `ede reaix `ed 4 oky F- a epi` 12 ,lynl .mze` wlgn epi` reaixy mixtqnd lk zveaw F idz :xcazn `ad xehdy egiked . F = { f 1 ,f 2 ,... } onqp . 12 z` wlgn ∞ X n =1 1 f n 1 :`ad oeieeiyd i` z` egiked :dkxcd ˆ N X n =1 1 n 2 !     X f ≤ N f ∈ F 1 f     ≥ N X n =1 1 n 5 libxz enekqe qpkzn dltknd xeh if` B- e A l miqpkzne miiaeig ∑ b n- e ∑ a n mixeh xy`ky epgked .(miiaeig gxkda `l j`) hlgda miqpkzn mixehdy dxwnl ef dgked z` aigxdl ji` e`xd . AB :wexita eynzyde qpkzn dltknd xeh dnl exiaqd :dkxcd ∞ X n =1 a n = ∞ X n =1 a + n-∞ X n =1 a-n 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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Infi2HW07 - 4 libxz `ede reaix `ed 4 oky F a epi` 12,lynl.mze` wlgn epi` reaixy mixtqnd lk zveaw F idz:xcazn `ad xehdy egiked F = f 1,f 2 onqp 12

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