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LEARNING GOAL: to use the Direct Comparison Test or the Limit Comparison Test to show

a given series converges or diverges by selecting an appropriate comparison series, verifying that both the

comparison series and given series have positive terms, determining whether the comparison series converges

or diverges, and comparing the two series' general terms either directly or via a limit.

7. Use the Direct Comparison Test or the Limit Comparison Test to determine whether the following series

converge or diverge:

(a)

n-1

1-2 √³+1²

n-1

n+3"

22

1+n6/nΞ

Ε

(1) Σ

htt

hea + Α

+2²² +1

/n? + 1 +8° + In(n)

5" – cos(n) – ne

Fig: 1

Fig: 2