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The question is in the picture!! Thank you in Advance

The question is in the picture!! Thank you in Advance-example-1
User Paul Huynh
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1 Answer

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Answer: Series diverges to infinity

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Step-by-step explanation:

The leading terms of the numerator and denominator are 5n^5 and 4n^5 respectively. They divide to 5/4. The n^5 portions cancel.

As n approaches infinity, the nth term of the sequence is going to approach 5/4 = 1.25 which is larger than 1.

Adding stuff to a series that's larger than 1, and doing so infinitely many times, means that the partial sums explode to infinity. The partial sums do not approach a finite value. Therefore, this series diverges to infinity.

User Decyclone
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