Give examples of the following: 1.an unbounded sequence that has a convergent subsequence . 2.an unbounded sequence that has no convergent subsequence . 3.a null sequence (an) such that the series ¡æ an does not converge . 4.a sequence which is not a cauchy sequence but has the property that for every ¦å > 0 and every n > 0 there exists n > n and m > 2n such that mod(an ¨c am) ¡ü ¦å . 5.two sequences (an) and (bn) such that the sequence (cn) defined by cn = an + bn converges to 1 but neither (an) nor (bn) converge. 6.a sequence (an) that tends to +ve infinity but is neither increasing nor eventually increasing

Find the common ratio of the sequence. -4, 8, -16, 32, a: -12b: -2c: 12d: -1/-2

Two researchers are attempting to create a new psychotherapy protocol that more reduces panic attacks. they believe that they have succeeded and are now in the clinical trial period of their protocol's development. they are working with several cohort groups, some of which have been through the new protocol, while others have done the standard protocol currently recommended. if these researchers are interested in evaluating the difference in the percentage of test subjects who successfully decreased their panic attacks in 2 months on the new protocol versus the percentage of test subjects who successfully decreased their panic attacks in 2 months with the traditional protocol, which of the following statistical tests would be most appropriate? a. analysis of variance (anova) b. correlation c. chi-square test d. paired t-test e. independent t-test

A33.33 percent decrease followed by a 50% increase. greater or larger that original amount?