Unformatted text preview: H‘H— BUI
ﬂu” 3,, r for all values of x for which the series con‘
n. 4. Let f be the function deﬁned by f(x) # Z
n=l {3) Find the radius of convergence of this series.
(b) Use the first three terms of this series to ﬁnd an approximation of f(l). (c) Estimate the amount of error involved in the approximation in part (b). Jystify your anSWer. n+1 n+1 n
a.)  um. _. 2' x n+0 . 3 n!
“.306 Mm n4” SHHOﬁ D! X“ Y1“
_ x I n x
' ns~i3(‘*‘ﬂi= iE'a a Series converges 1i l%'e[<i or" ixi< 0 radius O'F' COHVQV'SQHCE ‘15‘22: b)'F(U = gig—1.1.3.. _—. '%+%7‘:+w H—D 2" :% ‘ I a n i a
c.) The. aw’ﬂn series 15 alt"nosing? decreas‘lﬂﬁ and converaent. The. error commi'i‘i‘ed when am approximd‘ion is made b‘i‘" +rttnca+eoi series
is 'HME. anOIwi'e. mime. a1" 'Hne *iirst omiii’eoi +erm. ®To skew series is decreasing: n was»! n+1
n > (hti2 3 n
__ __ (n+1)
5“” .3"n! 3"“(Mm 9" 3w3 >7 :0 , 1 "‘ . .
since. (\ +77) } :5 am increasixg segues. witk Ii";
3 ‘2 e. 7044;) Series Comerges since. i" ! 4 radius 6i: ComergenceT i984 8C4 ...
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