## teachme1234 Group Title find the sum ∑_(n=1)^100▒2n 2 years ago 2 years ago

1. satellite73

hmmm

2. Australopithecus

is this summation censored?

3. teachme1234

no

4. satellite73

$\sum_{n=1}^{100}2n$?

5. teachme1234

yes

6. KingGeorge

$\sum_1^{100} 2n=2 \cdot \sum_1^{100} n=2\cdot {n(n+1) \over 2}$

7. KingGeorge

Where $$n=100$$

8. satellite73

$\sum_{k=1}^nk=\frac{n(n+1)}{2}$ so ... what king george said

9. teachme1234

still not getting it

10. Australopithecus

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

11. teachme1234

we are counting from 1 to 100 what is the nth term.

12. Australopithecus

100 terms sorry

13. teachme1234

2xn(n+1)/2 so i use this fromula to solve it.

14. colorful

in general $\sum_{i=1}^{n} i={n(n+1)\over2}$

15. Australopithecus

(2)100(100+1)/2 = 10100 proof https://www.wolframalpha.com/input/?i=summation+of+1+to+100+of+2n

16. Australopithecus

if you want to understand the formula I recommend just looking up sum of arithmetic formula on wiki

17. Australopithecus

or you can just accept it

18. colorful

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

19. colorful

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

20. teachme1234

okay so c=2 n=100

21. colorful

yes

22. teachme1234

okay got it thanks

23. colorful

welcome