Quiz 9: Mock IMO Algebra Contest

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Created by Isabelle Yeong (5th June 2015)

What is your name?

(First name, Last name)

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Your score report will be sent to your email account as you indicated in this section.

Please answer the following questions based on the series below:

Question 1: Do you think the expression on the denominator can be factored?

Yes.

No.

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Question 2: If we're asked to rewrite the general term of the series, which of the following concept would we use next?

A. Clearing the Fraction

B. Rationalizing the Denominator

C. Partial Fraction

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Question 3: Do you think the trigonometric substitution for the variable x would be useful in finding the sum for this problem?

Yes.

No.

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Question 4: Will you suspect that there is the possibility that this series telescopes?

A. No, there is no way this series telescopes.

B. This is definitely a telescoping series.

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Question 5: If this is a telescoping sum, would you consider to let the sum as S, and then cube both sides of the equation in your next step?

Yes.

No.

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Question 6: If this is a telescoping sum that the general term of the series can take the form such as f(n)-f(n-1), what would you do to find that second form to represent the general term?

A. I don't think this is a doable question.

B. I would try working with the first few terms by replacing n with 2, 3 or any other numbers to see where that leads me. and 6 (and so on) to see where that leads me.

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Question 7: If this is a telescoping sum, does there exist a closed form expression for this sum?

Yes.

No.

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Question 8: What is the answer to this problem?

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Question 9. Please rate the difficulty on this problem on a scale from 1 to 5 with 5 being the highest level of difficulty and 1 being the lowest level of difficulty.

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