1984BC4

# 1984BC4 - H‘H— BUI ﬂu” 3 r for all values of x for...

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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 1-i- 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 *i-irst omi-i-i’eoi +er-m. ®To skew series is decreasing: n was»! n+1 n > (ht-i2 3 n __ __ (n+1) 5“” .3"n! 3"“(Mm 9" 3w-3 >7- :0 , 1 "‘ . . since. (\ +77) } :5 am increasixg segues. wit-k Ii"; 3 ‘2 e. 7044;) Series Comerges since. i"| ! 4 radius 6i: ComergenceT- i984 8C4 ...
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