teachme1234
find the sum ∑_(n=1)^100▒2n
Delete
Share
This Question is Closed
anonymous
Best Response
You've already chosen the best response.
0
hmmm
Australopithecus
Best Response
You've already chosen the best response.
0
is this summation censored?
teachme1234
Best Response
You've already chosen the best response.
0
no
anonymous
Best Response
You've already chosen the best response.
0
\[\sum_{n=1}^{100}2n\]?
teachme1234
Best Response
You've already chosen the best response.
0
yes
KingGeorge
Best Response
You've already chosen the best response.
1
\[\sum_1^{100} 2n=2 \cdot \sum_1^{100} n=2\cdot {n(n+1) \over 2}\]
KingGeorge
Best Response
You've already chosen the best response.
1
Where \(n=100\)
anonymous
Best Response
You've already chosen the best response.
0
\[\sum_{k=1}^nk=\frac{n(n+1)}{2}\] so ... what king george said
teachme1234
Best Response
You've already chosen the best response.
0
still not getting it
Australopithecus
Best Response
You've already chosen the best response.
0
you can add them all up like
2(1) + 2(2) + 2(3)...
or you can just use a formula to solve for it which is much quicker
teachme1234
Best Response
You've already chosen the best response.
0
we are counting from 1 to 100 what is the nth term.
Australopithecus
Best Response
You've already chosen the best response.
0
100 terms sorry
teachme1234
Best Response
You've already chosen the best response.
0
2xn(n+1)/2 so i use this fromula to solve it.
colorful
Best Response
You've already chosen the best response.
0
in general \[\sum_{i=1}^{n} i={n(n+1)\over2}\]
Australopithecus
Best Response
You've already chosen the best response.
0
if you want to understand the formula I recommend just looking up sum of arithmetic formula on wiki
Australopithecus
Best Response
You've already chosen the best response.
0
or you can just accept it
colorful
Best Response
You've already chosen the best response.
0
the rules of summations are such that we can take constants out of the summation sign\[\sum_{i=1}^{n} Ci=C\sum_{i=1}^{n} i=C{n(n+1)\over2}\]where C is any constant
that is how we got our formula
colorful
Best Response
You've already chosen the best response.
0
The proof is quite easy if you know mathematical induction
if not, it's better to just accept it, or look up the formula for any arithmetic series the wiki way, as suggested by @Australopithecus
teachme1234
Best Response
You've already chosen the best response.
0
okay so c=2 n=100
colorful
Best Response
You've already chosen the best response.
0
yes
teachme1234
Best Response
You've already chosen the best response.
0
okay got it thanks
colorful
Best Response
You've already chosen the best response.
0
welcome