Integral Test

11.3integraltest

Ibset is a conn.nu
pisiiiFaecreasing
function on i x andlet an fin
if litenaxis convergent then Ian
is convergent theinfant
ii still is iii at
if I tenaxis divergent then an is divergent Sitextaxfor thesumEaan
mammen


iii itiI iii.ie
i ii
bytheintegraltest sincetheinterval converges the seriesconverges


tax ispositiveandcontinuous
i isgettinglargers otextis decreasing
1 extia ax
ethms
ftp Iht

ÉÉ 1
111 bytheintegraltestsincetheintegralconverges theseriesconverges




if EEi ii t
e
si is
decreasing
L ne
youns.msn
s Ifitau
Iat

t.iti ati
forwhichvaluesofp does he converges
let ten it when we wehave since we
niiyggiitiepgq.cat gtyntin
theorem the p series he convergeswhenps anddivergeswhen pct
note whenp i harmonicseriesobserved diverges
If It ie nudge the.liaqyrag
partials ums toestimatethevalue buttherewillbe
an error or a remainder
gien
Eanwithtens am in
mate
thentheremainder is
any

notonquizorexam given is find a value for nsuchthat in 0.000s


I si Ig t.li
an to antaco000s na s o.to 1000
ns viooo 31.0 weneed32terms