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Use properties of convergent sequences and the Comparison Lemma to prove that { [5(−1)n ]/n3 }...

Use properties of convergent sequences and the Comparison Lemma to prove that { [5(−1)n ]/n3 } converges in R.

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Answer #1

Given sequence   .

Let ,   .

Now consider the sequence ,  

As ,  

for all   .

By comparion lemma ,

As ,

So ,  

Hence the sequence converges and converges to 0 .

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If you have doubt at any step please comment .

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