207 



n n — 1 1 



i c tl 1 ïi — 1 1 



= ^(^'1 [ai A„ + a2 /i„-i + .. +a„ /h] + ^'/' [ai /«„ + •• + a«-i /'2] + • +^|f' ' 'M/*,, 

 From /ïm /i„ =: O if is evident that A/^ maj be cliosen, so 

 that \hkAri\ <i My, if jr=rl,2,... and lim.Mk = 0; putting ff„ = 

 =: jai|-[-|ö!2H- ■ . • 4-|«h| and Um.a„=:ö, we have: 



\Q\ <AW[\ai\.\hn\ + \a2\. \k„-i\ + . . . + |a„|.|/ti|] + 



+ A(P) [|ai| . |A„| + . . . + |a„_i| . |A2|] . + . . . + AU') . \cn\ . \h„\ 

 <^(;')il/l[|ai|fH+ .+|a„|]+^W;1/2[|ai| + .. + |a„_i|] + .. + ^(/')J/„|ai| 

 <;^(/')lfi a„ + Aip) M2 ö„_i + . . . + Aii') M„ ai 

 < a [Aip) Ml 4- AW ilf2 + . . . -I- Aip) M,,]. 



Now whatever be e ^ O il is possible to calculate k so that Mjc^i <^ — ; 

 further let M be chosen so that Mi<^M, then we have, if n^k: 



|Q|< [^(/'^ Ml + . . + A(^') yl/4] + 6 [A(ji>)_^ + . . . + ^1/')] 



< i1/ a [A'f 4- . . . + ^t,")] + f [^(/'+i) — A'ii'-^^)\ 



Hence : 



Q 



^(/'+i) 





A(p+i) — A'-P+^) 



n k 





= for Urn . A(p) = oo because A^p^ > AC') = n. 



Hence, if n is sufficiently great 



Q I 



Aip+^)\ 



Q 



£e + B 



and since e is arbitrary liin . ,, , , 



Therefore : 



= / 



P+Q 



nil . 



- -4- Urn 



Q 



,,,^00 Aip+i) „=„ .4<v+i) „=„ ^0^+1) „=„ .40'+i) 



n n It n 



== 5 . <. 



