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Math 1B Due date: Monday 25 April Name: _________________________ Take Home Quiz 3 Please show all your work on a separate sheet of paper. Neatly do the problems in order and leave enough space between problems for my comments and grading. You are allowed to get help with the problems and discuss them with your classmates but all work must be your own. 1. Show that lim x1/x = 1 x→∞ 2. Does the following sequence converge or diverge? Justify your answer: {n1/n } n = 1,2,3,4... 3. Does the following series converge or diverge? Justify your answer. ∞ ∑n 1/n n=1 4. Determine whether the geometric series is convergent or divergent. If it converges, find the sum. Justify your answer. 16 −12 + 9 − 27 81 + − ... 4 16 5. Find the sum of the geometric series. € ∞ ∑[2(0.6) k+1 − 3(0.4)k−1 ] k=2 6. For the following telescoping series, find a formula for the nth term of the sequence of partial sums {sn }. Then evaluate lim sn to obtain the sum of the series or state that the series diverges. n→∞ ∞ " n + 1% ' n & ∑ ln$# € n=1 €