Question

What’s the sum of the integers from 1 to 300?

Answer 1

well, we can either count them once, or twice ... which would you perfer

Answer 2

i dont know how finding integers work :/

Answer 3

lets take the set:\[1,2,3,4,...,297,298,299,300\]
do you agree that there are 300 elements in this set?

Answer 4

yes

Answer 5

lets take another set, but define it as:
\[300,299,298,297,...,4,3,2,1\]
would you agree that there are 300 elements of this set; and that it is just the first one turned around?

Answer 6

yes :)

Answer 7

then the sum of adding both sets would be 2 times the amount we need .... so lets add the elements together like this:
\[\begin{matrix}
&1&2&3&4&...&297&298&299&300\\
+&300&299&298&297&...&4&3&2&1\\
\hline\\
&301&301&301&301&...&301&301&301&301
\end{matrix}\]
would you agree that we have 300 elements of 301 each?

Answer 8

yes i agree

Answer 9

so, 301 added together 300 times is just multiplication:\[300(301)\]and that is twice the solution. therefore divide it in half:\[\frac{300(301)}{2}\]

Answer 10

in general: if you have \(n\) elements of an arithmetic sequence, then the sum of them amounts to:\[\frac{n(first+last)}{2}\]

Answer 11

ok sooo n is 300 ( 1 + 300 ) /2 ?

Answer 12

or n is 301?

Answer 13

correct

Answer 14

oh so n is 300 only? where did the 301 go?

Answer 15

we have 300 elements; first one is 1, last one is 300

the sum of the set is: 300(1+300)/2

Answer 16

ph ok so basically 300(301)/2 =45150

Answer 17

oh*

Answer 18

correct

Answer 19

thank you ^_^ ill keep in mind the formula thanks again

Answer 20

youre welcome

Answer 21

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graph of f(x) = 6 sin x + (sinx)^2 at which the tangent line is horizontal.

Answer 22

Prove by Induction
"The sum of the cube of any three consecutive integers is divisible by 9"

I confused with what is the basis step that I should take

Answer 23

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Answer 24

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Answer 25

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Answer 26

Choose the pair of events that is mutually exclusive.

(a). Even integers and multiples of 3
(b).

Answer 27

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Details and assumptio

Answer 28

How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Details and assumptio

Answer 29

How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Details and assumptio

Answer 30

How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Details and assumptio

Answer 31

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Answer 32

Quick question =)

Answer 33

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Answer 34

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Answer 35

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Answer 36

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Answer 37

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Answer 38

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Answer 39

Testing

Answer 40

help please!

Answer 41

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Answer 42

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