1 for convergence, you 2k5 +9k8 will use the Limit Comparison Test, comparing it to the p 1 series 9k² To test the series k=1 k=1 k=1 where p Now by the limit comparison test, the series ∞ 1 2/5 +9k8 = diverges converges O
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- Does the sequence an converge or diverge? Find the limit if the sequence is convergent. an=2+6n4/n4 + n4+4n3 does the sequence diverge? If the sequence converges. To what Iim n-->infinity an=?Identify two subsequences of ((−1)^n + 1/n) which converge to different limits. You should include explicit formulas for the selector functions.Pick one of your two subsequences and write a proof of the fact that it converges.2. Consider the series partial sum of infinity to k = 2 of (k^4 + 2k^2 + k −3)^(1/2)/(k^3 + 2k^2 + 6) .(a) Explain why the Limit Comparison Test is a good choice for determining convergence/divergence of theseries.(b) Use the Limit Comparison Test to determine whether the converges or diverges. Make sure to carefully apply the test and to explain your choice of a comparison series.
- Please show all work using clear explanation of your reasoning: Use the Comparisson Test to determine convergence or divergence of Σ∞n=1(1/(n2+10))Use the limit Comparison Test to determine the convergence or divergence of the series.∑_(n=1)^∞▒(2^n+1)/(5^n+1) Also see the attached picture of the problem, it is better. Thank you.∑∞ ((−1)^n−1(1−n)) /(3n−n^2) n=1 Find if the series converges or diverges! Find the limit if it converges.
- Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive.∑n=1∞enn!ρ=limn→∞|an+1an|= (Enter 'inf' for ∞.) ∑n=1∞enn! is:A. convergentB. divergentC. The Ratio Test is inconclusiveDetermine if the sequence converges of diverges, if it converges, find the limit. an = √1+4n2 / √1+n2{(1+3/n)n} converges or diverges. If it converges then determine it's limit. If not explain
- Determine the interval of convergence and the radius of convergence. Test endpoint convergence. S= Σ (-1)^n x^n/ 3^ncheck if the fixed point itteration converge or diverge for (x^3/3)+4 in interval [4,5]I am trying to find if this converges absolutly or conditionally, or diverges. I am not sure how to proceed when I get infinity/infinity. My steps are in the Image.