Test for convergence or divergence, using one of the tests listed below.0011n + 5n + 6n = 1convergesO divergesIdentify which test you used. (There is more than one correct answer, but you need select only one.)O nth-Term TestGeometric Series Testp-Series TestTelescoping Series TestIntegral TestDirect Comparison TestO Limit Comparison Test

Given query is to find series converges or diverges

Answered: Test for convergence or divergence,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Test for convergence or divergence, using each test at least once. Identify which test was used. (a) nth-Term Test (b) Geometric Series Test (c) p-Series Test (d) Telescoping Series Test (e) Integral Test(f) Direct Comparison Test (g) Limit Comparison Test
using any of the following methods, show wether series converges or not. ( p-series test, geometric series test, test for divergence, limit comparison test, ratio test, alternating series test, or integral test). say which one you used and make sure it will work with equation given.
a. Determine a suitable ?-series to compare with (the second equation) b. Do specify if you are using a common-sense comparison of two large-indexedterms of the series or if you are using the limit comparison of the ratio of the two terms.
Does the series from 3 to infinity for (ln(n))/(ln(ln(n)) converge conditionally, absolutely or diverge. Please use one of the following test to demonstrate the solution. If possible use more the one test Integral Test Comparison Test Limit Comparison Test Alternating Series Test Ratio Test Root Test Please show steps in detail Thank you
Select the FIRST correct reason why the given series diverges . A. Diverges because the terms don't have limit zero (nth Term Test for Divergence)B. Divergent geometric seriesC. Divergent p seriesD. Integral testE. Comparison with a divergent p seriesF. Cannot apply any test done so far in class
Indicate if the following series converge or diverge. You must identify all the tests you use and show all work needed to apply them. using either ratio test, power series test, root test, alternating series test, direct comparison test, limit comparison test, telescoping series.
Find the power series' convergence interval. (Don't forget to perform a convergence check at the interval's ends. Enter your response using interval notation if the answer is an interval. Enter your responses as a comma-separated list of values if the answer is a finite set of values.)
1. What is the center of the given power series? (This is what the book calls “a”.)2. Determine the radius of convergence (R).3. Determine the interval of convergence. NOTEFor any tests you use:1. Prove that any conditions of the test are met.2. Prove that the hypotheses of the test are satisfied.3. Clearly state your conclusion.• If you use a comparison test, clearly indicate which “similar series” you are comparing to, whether thesimilar series is convergent or divergent, and some proof or indication of how you know this.• When using inequalities to compare terms, show each step leading up to your final inequality.• Show all of the steps you took in evaluating any limits.
state whether the series converges or diverges and by which convergence test. Options: a. diverges-alternating series test b. converges ratio test c. converges alternating series test d. diverges integral comparison test e. diverges ratio test f. diverges alternating series test ∞∑n=1 (−1)n n --------- 5 n + 6 ∞∑n=1 5 n2 ---------- 1 + n8 ∞∑n=1 (−1)n n3 ----------- 5 + n4
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.) SIGMA n=1infinity (-1)n+1(x-5)n / n8n
Explore convergence of power series. Determine interval of convergence and Investigate endpoints.
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.

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