Evaluate this limit:

limit {(2+√2)n}
n→∞
where, {x} = x - floor(x)

The ε's (at intervals of 10 of n):
 
   n       ε
 

 10 0.00475765695916638669484253881501316224897131575942354737865785722131894750277164091018780378688115 
 20 0.00002263529974110434931423291293717059423353224894940328792545891970891654581638154138465800505134 
 30 0.00000010769099133608221857071962319512498566822825595102672841215892374631327162327040066544552234 
 40 0.00000000051235679436963862309187045242020708106066241797393585569383595516204503649813537349232464 
 50 0.00000000000243761786830889256706349802514658275945151479219864496238521248715333778242608380296195  
 60 0.00000000000001159734961494813546367005724947615011574918843631360603594905308021304024662296695378 
 70 0.00000000000000005517621110344361178416914999603457817831323761284692900571539518915684460916411950 
 80 0.00000000000000000026250948473673215586848293661194754579910313764294630558321445276637769360890932 
 90 0.00000000000000000000124893007690489610981692328612283981120561136394143384842411639487104871384696 
100 0.00000000000000000000000594198087189878950562815677134712453213746567314680782026811479852318609927 
110 0.00000000000000000000000002826990664642282999322079634062646497508670547998565169596778850754006153 
120 0.00000000000000000000000000013449851809133766590412625978860909694456594057787198950236711995910250 
130 0.00000000000000000000000000000063989781059481880769402041301908403011095123670790246453131652745541 
140 0.00000000000000000000000000000000304441427173177411151138777869760473342737434599558038799916287048 
150 0.00000000000000000000000000000000001448427874649014211145310081515142656884842863438976769882622855 
160 0.00000000000000000000000000000000000006891122957674461270926032459623675366153750416404262404428971  
170 0.00000000000000000000000000000000000000032785599096051154294878216815757924917462009993470250520031 
180 0.00000000000000000000000000000000000000000155982633699766971123034566120893742908516624257792111657 
190 0.00000000000000000000000000000000000000000000742111862730797681715996086958204751838939575243748225 
200 0.00000000000000000000000000000000000000000000003530713668201109874080393132409477619418883295673056 
210 0.00000000000000000000000000000000000000000000000016797924454340891181629555021099690964444705077518 
220 0.00000000000000000000000000000000000000000000000000079918762179746169818714023603374426268475153797 
230 0.00000000000000000000000000000000000000000000000000000380226055052432792386595400967025066302783926 
240 0.00000000000000000000000000000000000000000000000000000001808985136876588541171079326571562232671908 
250 0.00000000000000000000000000000000000000000000000000000000008606530725489460055026416814568389468810 
260 0.00000000000000000000000000000000000000000000000000000000000040946920800404260513423903875895075584 
270 0.00000000000000000000000000000000000000000000000000000000000000194811402702478202860898618092053035 
280 0.00000000000000000000000000000000000000000000000000000000000000000926845825792410853800272201524223 
290 0.00000000000000000000000000000000000000000000000000000000000000000004409614493155580001552199391692 
300 0.00000000000000000000000000000000000000000000000000000000000000000000020979433080602604245111966191 
310 0.00000000000000000000000000000000000000000000000000000000000000000000000099812945795294486530231577 
320 0.00000000000000000000000000000000000000000000000000000000000000000000000000474875756177880149448264 
330 0.00000000000000000000000000000000000000000000000000000000000000000000000000002259295946119091742421 
340 0.00000000000000000000000000000000000000000000000000000000000000000000000000000010748955080869902656 
350 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000051139840944267583 
360 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000243305820159156 
370 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000001157565628485 
380 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000005507300168 
390 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000026201844 
400 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000124659

Edited on November 17, 2022, 10:16 am

Posted by Charlie on 2022-11-17 10:04:25