What is the range of the function f(x) = |x| – 3?
1 answer:
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We can use the sum of an aritmetic sequence
the sum from n=1 to n=r when the first term is a1 and the nth term is an is
first term is 1
last term is 100
there are 100 terms so n=100
so the sum is
S=5050
now you want us to divide by 10
5050/10=505
fun fact, gauss (famous math guy) did this when he was younger, legend has it that he was assigned this as an in class assigment to kill time but gauss found a neat pattern, he noticed that adding the end terms wer giving the same sum, example, 100+1=101, 2+99=101, etc, so he just needed to find al the pairs and add them all up
answer is 505
the result is 505
the sum from n=1 to n=r when the first term is a1 and the nth term is an is
first term is 1
last term is 100
there are 100 terms so n=100
so the sum is
S=5050
now you want us to divide by 10
5050/10=505
fun fact, gauss (famous math guy) did this when he was younger, legend has it that he was assigned this as an in class assigment to kill time but gauss found a neat pattern, he noticed that adding the end terms wer giving the same sum, example, 100+1=101, 2+99=101, etc, so he just needed to find al the pairs and add them all up
answer is 505
the result is 505
The sequence is geometric, so
for some constant r. From this rule, it follows that
and we can determine the first term to be
Now, by substitution we have
and so on down to (D)
(notice how the exponent on r and the subscript on a add up to n)