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