Download A Banach space version of Okada's theorem on summability of by Gawronski W., Shawyer B. L., Trautner R. PDF

By Gawronski W., Shawyer B. L., Trautner R.

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Extra info for A Banach space version of Okada's theorem on summability of power series

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L a rc tg (-) ,2 7T arctg (-) — l i m ( ---------- ^ + -----------2 - + . . + /;—>x 1 + // 4 2 + /7 ' /? + // 1 n 2 arctg — ¿//r/g — arctg — . lim [----- ^ + -------- * + ... + ------ 2 - ] n—>rc 2 4" n 1 + a/ ^ i _j_ ^ n _"arctg( - ) , , Umy _ i « //— >*' ÁmmJ . , =1 - . /" /? Y = <7/'C7g a*. +. ^ sec2 OdO \ + tg~0 TC 47 Sucesiones n it f 4 ln(l Como i + t g d = + tgü) 4 sec" n n n eos (i + sen6 71 sen (— ~ 0 ) + sen O i eos 0 6 2sen —cos(— ~ 0) \/~2 cos(~- - 0 ) eos <9 eos # R ■n 0) v 2 cos( -dO =| 4 l n ----— - 4 eos 0 Tt ln(l + jt) dx - ln(l + tg6)d0 OdO sec~ O eos í •— ti j^4 ln(l 1+ x + tg 0 ) d 0 n K ».

L n « ! " ^ K +\ - K w—>x ln(/7 + \ )n^ ] - ln n n /? 77 ln(/7 +1) 77. ln(— —) 4- ln(/7 4-1) 7? 13. Estudiar la convergencia ó divergencia de la sucesión (2w + 5)2"+5«"~3 (4 h + 1)',+2(« + 3)2" Solución /-v \2 ii+5/i . , = (2/? + 5)2" " V ~ 3 (4« + l)',+2(K + 3)2" ( l n) (1 + — ) ln n (4/j)«+2(1 + ± )»+2n2»(1 + 2 )2» 4/7 77 Eduardo Espinoza Ramos 30 2 2"+5/i2"+V _V 2"(1 + — ) 2"+5 2 2n+5n 2+” (l + 2n 4 "+2nl,+2 (1 + -^-)"+2 (1 + - ) 2" 4n — ) 2" +s 2n 22n+4 > r 2 (1 + 4/i n 2(1 +-—-)2,l+5 2n (l + - - )"+3(1+ - ) 2 4/?

4 - — -— ] — = 0 4- j i m \ /;~»x n H->« 1 //— X L 14 --n i _j. n 2 - ln 1 - ln 2 - 0 = ln 2 o *4 -1 i11 m /;~>x 22 r* i i C alcu lar / o 1 1 1 n n 4-1 // 4- 2 ( — f"---------- f r / n 1 ). f-... 4 2n , . — 1n ~ fl n l i m ( — ------- 4- — ------- --4- ... + — -------- 7 ) />—»x 4- J // 4- 2■*>4- /7 Solución l i m [” 7 ------ 7 4-... Y - lim //—>x ‘j'i = a r e / ? 1- T = a /r /g -v/ 1 4- A' 4 tcrga0= 4 0 = — 1 4- ( n u ' / 0 4 -... L a rc tg (-) ,2 7T arctg (-) — l i m ( ---------- ^ + -----------2 - + .

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