Question

find the sum ∑_(n=1)^100▒2n

Answer 1

hmmm

Answer 2

is this summation censored?

Answer 3

no

Answer 4

\[\sum_{n=1}^{100}2n\]?

Answer 5

yes

Answer 6

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

Answer 7

Where \(n=100\)

Answer 8

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

Answer 9

still not getting it

Answer 10

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

Answer 11

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

Answer 12

100 terms sorry

Answer 13

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

Answer 14

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

Answer 15

(2)100(100+1)/2 = 10100
proof

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

Answer 16

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

Answer 17

or you can just accept it

Answer 18

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

Answer 19

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

Answer 20

okay so c=2 n=100

Answer 21

yes

Answer 22

okay got it thanks

Answer 23

welcome