MATH 105 Midterm: MATH 105 2011 Winter Test 2

• School: UBC
• Department: Mathematics
• Course: MATH 105
• Professor: All

Document Summary

Special instructions: a formula sheet is attached to this exam. No books, notes, or calculators are allowed: show all your work. A correct answer without accompanying work will get no credit: if you need more space than the space provided, use the back of the previous page. Where boxes are provided for answers, put your nal answers in them. Page 2 of 19 pages: (a) find the radius of convergence of the series. Xk=0 ( 1)k2k+1xk. (6 points) (b) you are given the formula for the sum of a geometric series, namely: Use this fact to evaluate the series in part (a). 1 + r + r2 + = Page 3 of 19 pages (c) express the taylor series of the function about x = 0 in summation notation. f (x) = ln(1 + 2x) (8 points) Page 4 of 19 pages: this problem contains three numerical series. For each of them, nd out whether it converges or diverges.