MATH 101 Quiz #5 (v.A2) Last Name: Friday, March 18 First Name: Grade: Student-No: Section: Very short answer question 1. 1 mark Does the series ∞ X n=2 n2 √ converge? (Answer “yes” or “no” in the box.) 3n2 + n Answer: Short answer questions—you must show your work 2. 2 marks Relate the number 0.53̄ = 0.5333333 . . . to the sum of a geometric series, and use that to represent it as a rational number (a fraction or combination of fractions, with no decimals). A calculator-ready answer is acceptable. Answer: 3. 2 marks Show that the series ∞ X n=2 3 converges. n(log n)5/4 Long answer question—you must show your work yy 0 1 4. 5 marks Find the solution to the differential equation x = that satisfies y(0) = 3. e − 2x y Solve completely for y as a function of x.