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sineoko [7]
3 years ago
5

Ellipsis a set of three dots at the end of a number used to indicate that the number will infinitely continue in the same patter

n
irrational number a number that, when in decimal form, does not terminate or repeat
rational number a number that can be written as a ratio in fraction form
repeating decimal a decimal whose digits to the right of the decimal point repeat indefinitely
terminating decimal a decimal that ends
vinculum a horizontal bar used in mathematical notation; in fractions, it is the bar that separates the numerator from the denominator; in repeating decimals, it indicates a group of repeating numbers
Mathematics
1 answer:
alexdok [17]3 years ago
3 0

Answer:

Match the vocabulary words to the proper definition.

1. a decimal that ends  

2

repeating decimal  

2. a decimal whose digits to the right of the decimal point repeat indefinitely  

1

terminating decimal  

3. a set of three dots at the end of a number used to indicate that the number will infinitely continue in the same pattern  

4

irrational number  

4. a horizontal bar used in mathematical notation; in fractions, it is the bar that separates the numerator from the denominator; in repeating decimals, it indicates a group of repeating numbers  

6

vinculum  

5. a number that can be written as a ratio in fraction form  

3

ellipsis  

6. a number that, when in decimal form, does not terminate or repeat  

5

rational number

Step-by-step explanation:

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Let

P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

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So, the base case is ok. Now, we need to assume P(n) and prove P(n+1).

P(n+1) states that

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Since we're assuming P(n), we can substitute the sum of the first n terms with their expression:

\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}

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P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}

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