1. a) Find using integration by parts. Does the improper integral converge? b) What can you...

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1. a) Find $\int (\frac{ln(x)}{x^{3}})dx$ using integration by parts. Does the improper integral pinsinity In(x)}dz converge?

b) What can you say about the infinite series $\sum_{2}^{infinity}\frac{ln(n)}{n^3}$ using the improper integral in the previous part? Estimate the partial sum S₁₀₀ = 100 In(n) 2 73 . Find upper bound for R100 = n=101 and use the integral test.

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- -ਤੇੜੇ | ਕੰਨ ਦੇ it is finite , so it is converges ੪} by using integral test flokdx is converges 3 is converges Sun - 12 -0.1

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