Solved 1 15 15pts Determine If The Following Series Is Chegg 1. (15,15pts) determine if the following series is absolutely convergent, conditionally convergent or divergent. make sure that you state the name of the series or the series test you used and justify your answer. (b) ∑n=1∞(−nlnn)n. (15 points) determine if the following series converges or diverges. if the series converge, determine if it converges absolutely. indicate the name of the test that you are using and where is your work checking if the conditions for its application are satisfied. (a) (6 points) ∑ k = 1 ∞ (− 1) k k 2 6 k . (b) (5 points) ∑ l = 1 ∞ l.
Solved 1 15 15pts Determine If The Following Series Is Chegg 1 p n 4 first, we show the absolute series is divergent. note that x1 n=1 1 p n 4 ˇ x1 n=1 1 p n which is a divergent p series with p= 1 2 <1. next, check: lim n!1 1 p n 4 1 p n = lim n!1 p n 4 = lim n!1 1 1 4 p n = 1 which is nite and non zero. therefore, these two series share the same behavior. since x1 n=1 1 p n is the divergent p. \sum {n=1}^ {\infty} 4^ {n 1}5^ { n}. n=1∑∞ 4n 15−n. determine whether the geometric series is convergent or divergent. justify your answer. converges; the series is a constant multiple of a geometric series. n n goes to infinity. diverges; the series is a constant multiple of the harmonic series. if it is convergent, find its sum. 1. (15,15pts) determine if the following series is absolutely convergent, conditionally convergent or divergent. make sure that you state the name of the series or the series test you used and justify your answer. (a) ∑n=2∞n3−2 (−1)n (b) ∑n=1∞ (−nlnn)n. your solution’s ready to go!. Determine whether the series is convergent or divergent: $\sum {n=1}^\infty \frac{n 5^{}}{{(n^{7} n^{2})}^{1 3}}$ 2 is this series: $\sum {n=1}^{\infty}{{1 \over n} \cos{(n)} \sin{(nx)}}$ convergent?.
Solved 1 15 15pts Determine If The Following Series Is Chegg 1. (15,15pts) determine if the following series is absolutely convergent, conditionally convergent or divergent. make sure that you state the name of the series or the series test you used and justify your answer. (a) ∑n=2∞n3−2 (−1)n (b) ∑n=1∞ (−nlnn)n. your solution’s ready to go!. Determine whether the series is convergent or divergent: $\sum {n=1}^\infty \frac{n 5^{}}{{(n^{7} n^{2})}^{1 3}}$ 2 is this series: $\sum {n=1}^{\infty}{{1 \over n} \cos{(n)} \sin{(nx)}}$ convergent?. Let’s take a look at some series and see if we can determine if they are convergent or divergent and see if we can determine the value of any convergent series we find. example 1 determine if the following series is convergent or divergent. if it converges determine its value. ∞ ∑ n=1n ∑ n = 1 ∞ n. The series is divergent if the limit of the sequence as n n approaches ∞ ∞ does not exist or is not equal to 0 0. since its numerator approaches a real number while its denominator is unbounded, the fraction 1 n 1 n approaches 0 0. the test is inconclusive because the limit is 0 0. For each of the following series, if the series is positive term, determine whether it is convergent or divergent; if the series contains negative terms, determine whether it is absolutely convergent, conditionally convergent, or divergent. By ratio test, the series converges for jx 3j=3 <1 and diverges for jx 3j=3 >1. hence the radius of convergence is r= 3 and the interval of convergence is ( 6;0), possibly with one or both endpoints. now we check each endpoint. for x= 6, we observe that the series x1 n=1 ( 1)n ndiverges by the nth term divergence test since lim n!1.