Exercise 2.6.3. If (xn) and (yn) are Cauchy sequences, then one easy way to prove that (xn + yn) is Cauchy is to use solution the Cauchy Criterion. By Theorem 2.6.4, (xn) and (yn) must be convergent, and the Algebraic Limit Theorem then implies (xn + yn) is convergent and hence Cauchy. (a) Give a direct argument that (xn + yn) is a Cauchy sequence that does not use the Cauchy Criterion or the Algebraic Limit Theorem. (b) Do the same for the product (xn n).

In 2000, for a certain region, 27.1% of incoming college freshman characterized their political views as liberal, 23.1% as moderate, and 49.8% as conservative. for this year, a random sample of 400 incoming college freshman yielded the frequency distribution for political views shown below. a. determine the mode of the data. b. decide whether it would be appropriate to use either the mean or the median as a measure of center. explain your answer. political view frequency liberal 118 moderate 98 conservative 184 a. choose the correct answer below. select all that apply. a. the mode is moderate. b. the mode is liberal. c. the mode is conservative. d. there is no mode.