Math 1ZA31st Sample Test for Suggested Problems #4Name:___________________________________________(Last Name) (First Name)Student Number:Tutorial Number:_________________________________________This test consists of 26 multiple choice questions worth 1 mark each (no part marks). Allquestions must be answered on the COMPUTER CARD with an HB PENCIL. Marks will notbe deducted for wrong answers (i.e., there is no penalty for guessing). You are responsible forensuring that your copy of the test is complete. Bring any discrepancy to the attention of theinvigilator. Calculators are NOT allowed.1.Which of the following series converge?(i) (ii) 8œ"8œ"∞∞8"#Ð#8"Ñx8"†$†&†(† â †Ð#8"Ñ8Ð"Ñ(a)(b)(c)(d)(i) only (ii) only (i) and (ii) neither2.Which of the following series are absolutely convergent?(i) (ii) 8œ"8œ"∞∞88 #8 "8$8Ð"ÑÐ"Ñ#$8(a)(b)(c)(d)(i) only (ii) only (i) and (ii) neither3. Find the interval of convergence of8œ"∞8#8Ð$B #Ñ8 "(a)(b)(c)(d)(e)Ð∞ß ∞ÑÒ ß ÓÒ ß ÑÒ"ß ÓÒ"ß Ñ"#"#""$$$$$$4. If is convergent, what can you conclude about the convergence of the following8œ!∞88- #series?(i) (ii) 8œ!8œ!∞∞8888- Ð#Ñ- Ð$Ñ(a)(b)(c)convergent, nothing convergent, convergent nothing, divergent(d)(e)nothing, nothing convergent, divergent5. Find the radius of convergence of8œ"∞8Ð8 "ÑxÐ$B "Ñ(a)(b)(c)(d)(e)∞!""#$$
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