Question

Question about summation notation...

Answer 1

Does it matter what letter is under the sigma??? \[\sum_{x=9}^{10}(5x+4)\] or if I had
\[\sum_{t=9}^{10}(5t+4)\] or \[\sum_{n=9}^{10}(5n+4)\]

Do they all mean the same thing?

Answer 2

@Directrix

Answer 3

@amorfide @ganeshie8 @phi

Answer 4

Like if I had to find the sum of them, it would be the same for all of them right?
I gtg but I'll be back later so please answer it, but I wont be back for a while...

Answer 5

Cuz you see how under the sigma sign there's a t,n, and x. Does it matter what letter it is?

Answer 6

it does not matter,answer will be same because we are concerned with their values and they are 9 and 10 for each x or t or etc.

Answer 7

@Setsuna-Yuregeshi the letters don't matter because they'll be replaced with numbers anyway

So say you had \[\Large \sum_{x=9}^{10}(5x+4)\] you would have `(5x+4)` added up from x = 9 to x = 10. Basically 2 copies of `(5x+4)`. You replace the x in the first copy of `(5x+4)` with 9. The second copy has x replaced with 10.


\[\Large \sum_{x=9}^{10}(5x+4) = (5*{\color{red}{9}}+4)+(5*{\color{red}{10}}+4)\]

\[\Large \sum_{x=9}^{10}(5x+4) = (45+4)+(50+4)\]

\[\Large \sum_{x=9}^{10}(5x+4) = 49+54\]

\[\Large \sum_{x=9}^{10}(5x+4) = 103\]


These steps will be identical if you replace x with any other letter. The letter x is just a placeholder.

Answer 8

Ooh, ok thanks!!!