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Katena32 [7]
3 years ago
13

What is the sum of n natural numbers: 1+2+...+n?

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
5 0

If

S=1+2+\cdots+(n-1)+n

then we also have

S=n+(n-1)+\cdots+2+1

Pairing up the terms, we can find that

2S=(1+n)+(2+n-1)+\cdots+(n-1+2)+(n+1)

2S=(n+1)+(n+1)+\cdots+(n+1)+(n+1)

S consists of n terms, so there are n copies of n+1 in the sum 2S. Then we find an immediate closed form for the sum:

2S=n(n+1)\implies S=\dfrac{n(n+1)}2

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Determine the value(s) for which the rational expression 2x^2/6x is undefined. If there's more than one value, list them separat
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Answer:

0

Step-by-step explanation:

Hello, dividing by 0 is not defined. so

\dfrac{2x^2}{6x}

is defined for x different from 0

This being said, we can simplify by 2x

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Thank you

4 0
3 years ago
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Answer:

A= 13  B=13.1

Step-by-step explanation:

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7 0
3 years ago
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The answer to your question is  x = -3

6 0
3 years ago
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8
konstantin123 [22]

Answer:

f(x) = 7

Step-by-step explanation:

since an even function is defined as a function with the following rule. f(-x) = f(x) for all x in the domain of f(x). It would be odd if f(-x) = -f(x) for all x in the domain of f(x). If f(-x) ≠ -f(x), than it is neither. these are all known as the parity of a function.

you can apply these rules to all of given functions like this. (-x-1) ≠ -(x-1) so it is neither. 8(-x) = -(8x) so it would be odd. 2(-x)-(-x) = -(2x-x) so it is odd as well. This would make f(x) = 7 the only option, as there are no x variables in the equation so 7 = 7.

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3 years ago
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Step-by-step explanation:

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