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Give an example of a sequence that converges to 0 with order alpha= 10

Give an example of a sequence that converges to 0 with order alpha= 10
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Answer #1

Answer: Define a sequence of real numbers as

and

It follows from the definition of the sequence that the order of the sequence is .

Now, we show that the sequence converges to

For, let be a positive real number. Since , if we take , then

whenever

Thus, the sequence converges to

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