{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

M138.W09.assmt7

# M138.W09.assmt7 - MATH 138 Assignment 7(1 page Winter 2009...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 138 Assignment 7 (1 page) Winter 2009 Submit all problems marked * by 8:20 am. E‘iday, March 13 th *1. For each series. apply the 11 Term Test and hence state whether the series diverges. or might converge. oon+1 co 1 oo 1 00 TI 00 1 1. - —— 1 ' *2. For each series in problem 1 which you found might converge, apply the Integral Test or the Comparison Test to determine whether the series converges or diverges. n' 3. *a) Use the Comparison Test to show that the series :33? 2diverges. n. =3 71! b) Generalize your argument in a) to show that 2b— diverges for any b > 0. "=1 lnn COHVCI‘ CS. 113/2 g 4. 21) Use the Integral Test to show the series :— ‘ n: 2 1)) Apply the Corollary to the Integral Test (page 86 of Course Notes, or text page 701) to determine . an upper bound for the error if the series in a) is approximated by 3100. (DO NOT find 8100.) 11171 c) Determine all values of p such that Zn], —— converges 71:2 *d) Itepeat part a) for the series 2716‘". 11:1 *e) Repeat part b) for the series in d). but assume that series is approximated by S5. cos2 n , 1s convergent by compaiing to a suitable geometric series *5. a) Show that Zen 71:16 1)) Find an upper bound on the error if S4 is used to approximate the sum of the series in a). 6. By comparison to an appropriate p-series, detemine whether each series converges or diverges. *1) i n2 *b) i arctan(n) e) Z n —- 1 L 71:2 ”5/2 — 1 11:1 "2 71:2 (71. + 1);: 7. *a) Find the partial sum SN of each series using partial fractions or log rules. Hence determine whether the series converges, and if so, ﬁnd its sum. (See Example 6, page 691 of your text.) *. 0° 2 1... 0° 11 °° 1 02m ("Shh“) ("02m n=1 ":1 (Submit parts (i) and (11) only.) b) Criticize the following calculation. in which adjacent terms are cancelled indefinitely. oo 00 ‘ . , t 2* ”+1110. fan—31+ +213):(-g+§)+(_§+g)+(_§+51)1...=_§ n=1 This illustrates that we cannot treat series as ﬁnite sums. ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online