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Chapter 1: Q5MP (page 1)

Test for convergence:鈭�n=2鈭�(n-1)21+n2

Short Answer

Expert verified

The series鈭�n=2鈭�(n-1)21+n2 diverges.

Step by step solution

01

Concept used to prove that the series diverges

Conditions of convergence for the series 鈭�n=1鈭�anare:

limn鈫�鈭�an=0

02

Calculation used to show that the series ∑n=2∞(n-1)21+n2  diverges

nthterm of the series is,an=(n-1)21+n2

Apply limit in nthterms of the series as follows:

limn鈫�鈭�an=limn鈫�鈭�(n-1)21+n2limn鈫�鈭�an=limn鈫�鈭�n21-1n2n21n2+1limn鈫�鈭�an=limn鈫�鈭�1-1w21a2+1limn鈫�鈭�an=11limn鈫�鈭�an=1

Thus, this does not prove the second condition of the convergence as limn鈫�鈭�an鈮�0.

Hence, the series diverges.

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Most popular questions from this chapter

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