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# Tutor profile: Jessica R.

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Jessica R.
Student at Yale University
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## Questions

### Subject:Pre-Calculus

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Question:

What are sequences and series, and how are they different?

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Jessica R.

A sequence is simply a list of numbers. Often, the sequence will be listed as a function, where the x input will determine the y output. In this case, each y output would become a number in the sequence. A series, however, is a summation of a sequence. For example, if the sequence is: 1, 2, 3, 4, 5, then the corresponding series would be: 1 + 2 + 3 + 4 + 5. A series is merely the sum of all the numbers in a sequence. When we involve functions in our sequences, the series can get slightly more complicated, but the basic principle is always the same.

### Subject:Writing

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Question:

Long essays: how do you write an analysis in a long essay or document-based question, especially when it is an in-class essay with a time constraint?

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Jessica R.

### Subject:Algebra

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Question:

Understanding exponents: Why is anything, raised to the power of 0, equal to 1?

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Jessica R.

In order to understand this, we have to look at exponents as a pattern. Let's take the number 2. 2 raised to the first power equals 2; 2 raised to the second power equals 4; and 2 raised to the third power equals 8. As we increase the power by 1, the answer yielded is doubled, or multiplied by 2 -- which is what makes the pattern exponential. Therefore, we can look at this very same pattern, but backwards. As we decrease the power (from third, to second, to first), the answer yielded will be cut in half, or divided by 2 (it goes from 8 to 4 to 2). So if we decrease the power again, from the first power to the zero power, it only makes sense to continue to divide the answer by 2. 2 raised to the first power equals 2, and therefore 2 raised to the zero power equals 1 (which is half of 2). We can use this pattern to determine the solutions for negative exponents. Also, we can use this pattern to prove this theory for any number (but instead of multiplying and dividing by 2, we would multiply/divide by the whatever number we are using).

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