Solved For Each Of The Following Series A Determine Chegg 3. (15 points) determine whether the following series converge or diverge. clearly circle either con verge or diverge, note which convergence test is used, and then use the remaining space to show the work required by the test. do Σηe ην diverge (a) converge tests used: 2" (n! (2n)!. For each of the following, say whether it converges or diverges and explain why. 1. p ∞ n=1 n3 5 3 answer: notice that n3 n5 3 < n3 n5 = 1 n2 for all n. therefore, since p 1 n2 converges (it’s a p series with p = 2 > 1), the series p n3 n5 3 also converges by the comparison test. 2. p ∞ n=1 3n 4n 4 answer: notice that 3 n 4n 4 < 3 4n.
Solved 2 15 Points For The Following Series Determine Chegg Determine if the series converges absolutely, converges conditionally, or diverges. find the exact value for the sum of the convergent series. $$1 \frac{1}{5} \frac{1}{5^2} \frac{1}{5^3} \frac{1}{5^4} \frac{1}{5^5} \frac{1}{5^6} \frac{1}{5^7} \frac{1}{5^8} $$ i have no clue where to start. Question: 3. (15 points) determine whether the following series converge or diverge. clearly circle either con verge or diverge, note which convergence test is used, and then use the remaining space to show the work required by the test. ne converge diverge (a) n= tests used: 2"(n!)?. Determine whether each of the following series converges or diverges. name any convergence test(s) you use, and justify all of your work. (a) x1 n=1 nsin 1 n diverges by nth term divergence test since lim n!1 nsin 1 n 1= lim0 x!1 xsin 1 x = lim x!1 sin 1 x 1 x l= lim 0h x!1 cos 1 x 1 x2 1 x2 = lim x!1 cos 1 x = 1 6= 0 (b) x1 n=1 3 n3 sin2(3n. 3 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.
Solved 3 15 Points Determine Whether The Following Series Chegg Determine whether each of the following series converges or diverges. name any convergence test(s) you use, and justify all of your work. (a) x1 n=1 nsin 1 n diverges by nth term divergence test since lim n!1 nsin 1 n 1= lim0 x!1 xsin 1 x = lim x!1 sin 1 x 1 x l= lim 0h x!1 cos 1 x 1 x2 1 x2 = lim x!1 cos 1 x = 1 6= 0 (b) x1 n=1 3 n3 sin2(3n. 3 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. 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. (15 points) determine whether the following series converges or diverges. for full credit, you must tase a convergence test to justify your result. this problem has been solved!. Question: 3) (15 points with 3 points for each) test the following series for convergence or divergence. determine whether the following series converge or diverge. state the test or comparison that was used. show all steps. a) ∑n=1∞3n41 b) ∑n=1∞n2 3(−1)n(n 2) c) ∑n=1∞sin(n2) d) ∑n=1∞(n 3)!n2 1 e) ∑n=1∞((2n2 5)(n2 3))n. Determine if the series \( \displaystyle \sum\limits {n = 0}^\infty {{a n}} \) is convergent or divergent. if the series is convergent determine the value of the series. \(\displaystyle {s n} = \frac{{5 8{n^2}}}{{2 7{n^2}}}\) solution.