Let a,-1- s(n) and consider the series \'olan, which one of these state- ments d

Question

Let a,-1- s(n) and consider the series 'olan, which one of these state- ments describes the best approach to determining whether the series con- verges or diverges? Since 0 1+cos(n) 2 for all n. we should compare with n=1 TT to see that the series 01 an converges O Since 1-cos( n) 0 as n oo. the series will diverge. None of these statements, is decreasing, we should use the Leibniz test to determine whether the series converges As the terms a are eventually positive and the signs of the an do not alternate +,-,+,-.+,... we should apply the ratio test

Explanation / Answer

Option a should bd correct approach. As,

In 2 nd option , numerator does not go to zero. But whole expression does go to zero as n tends to infinity.

In 4 th option , only denomarator is decreasing not whole series. And it s not an alternate series. Cant apply libnitz test.

In last option, we can apply ratio test but it will be difficult to calculate limit as cos term will be there.

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