2 Use the comparison test to demonstrate the absolute convergence of the following series, by comparing them to series shown to converge in this chapter (a) Py n1 ln n2 n4 (b) Py n1 ln n np for p 2 (c) Py n11n1 sinn np , for p 1, where for sinn, n is understood in radians (i e , p radians 180) (d) Py n11n1an for 0 a 1

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Question: 2. Use the comparison test to demonstrate the absolute convergence of the following series, by comparing them to series shown to converge in this chapter:

2. Use the comparison test to demonstrate the absolute convergence of the following series, by comparing them to series shown to converge in this chapter:

(a)

Py n¼1 ðln nÞ2 n4

(b)

Py n¼1 ln n np for p > 2

(c)

Py n¼1ð1Þnþ1 sinðnÞ

np , for p > 1, where for sinðnÞ, n is understood in radians (i.e., p radians ¼ 180)

(d)

Py n¼1ð1Þnþ1an for 0 < a < 1

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