If the individual terms of a series correspond to a function satisfying the conditions of the integral test, then the convergence or divergence of the corresponding improper integral of tells us whether the series converges or diverges. What is the “easiest” way for a series to diverge?

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This is known as the integral test, which we state as a theorem. Theorem 13.3.3 Suppose that $f(x)>0 We could of course use the integral test, but now that we have the theorem we may simply note that this is a $p$-series with $p>1$. Determine whether each series converges or diverges.= diverges Since the integral diverges, then the series also diverges. 17.(4 points) Use the comparison test to determine whether the series ¥ å k=1 lnk k converges or diverges. Solution: For k > 3, lnk > 1, so lnk k > 1 k. å 1 k is the harmonic series and diverges, so by the Comparison Test, å lnk k diverges. 18.A function f is deﬁned by ... To determine if a series diverges or converges, we can use the Nth term test for divergence by finding . then the series either diverges or converges with the integral . Generally we use the Ratio Test to determine the divergence/convergence of series containing factorials, exponents...

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The critical values determine turning points, at which the tangent is parallel to the x-axis. If so, do they determine a maximum or a minimum? And what are the coördinates on the graph of that maximum or minimum?

Problem 2 Determine whether the given series converges or diverge. Problem 3 Find the sum of the series. Problem 5 (a) State the integral test. Нуроthesis: Continuous. Conclusion. (b) Determine the series. k=2 klnk. is convergent or divergent. X In X.The idea behind the limit comparison test is that if you take a known convergent series and multiply each of its terms by some number, then that new series also converges. And it doesn’t matter whether the multiplier is, say, 100, or 10,000, or 1/10,000 because any number, big or small, times the finite sum of the original series is still a ... Determine whether the following series converge or diverge. If a series converges and the terms are not eventually positive, determine whether or not the convergence is absolute. 1. X1 n=1 n n3 +1 Converges by direct or limit comparison to P n 1 2. 2. X1 n=1 n2 +1 n3 +1 Diverges by limit comparison to P n 1. 3. X1 n=1 n3 5n Converges by the ...