Question

I want to learn about Sigma Notation. I know that it's used for finding the sum of a sequence. How do you write it?

Answer 1

\[\text{\sum}\longrightarrow \sum\]

Answer 2

No, not latex.. I mean, how exactly is it written?

Answer 3

What is the number above the term and below?

Answer 4

\[\large \sum_{n=1}^n n = 1+ 2+3+4+\ldots+n\]

Answer 5

What is meant by this?

Answer 6

It's sum of first \(n\) natural numbers.

Answer 7

Rather, representation of sum of first \(n\) natural numbers.

Answer 8

I did understand. But why is n equal to 1 + 2 + 3 + 4...n

Answer 9

Shouldn't it be:

\(\Large \color{purple}{\rightarrow \sum_{n = 1}^{n}(1 + 2 + 3 + 4....n) }\)

Answer 10

Hmm
\[\large 1 + \sum_{n=2}^n n= 1 + 2+\ldots +n\implies 1 + 2+3+\sum_{n=4}^n=1+2+\ldots +n \]
Do you get it now?

Answer 11

Sorry.

Answer 12

It's supposed to be \[1+2+3+\sum_{n=4}^nn=1+2+\ldots+n\]

Answer 13

Oops, that's even more confusing @Ishaan94

Answer 14

If it were for your representation then it would be,
\[\large\sum_{n=1}^n\left(1+2+3+\ldots+n\right) = 1 +\left(1+2\right)+\left(1+2+3\right)+\ldots +\left(1+2+\ldots +n\right)\]

Answer 15

I mean what do you mean by the n = 4 in the bottom, and n on the top?

Answer 16

argh, bad latex :/

Answer 17

lol :D

Answer 18

Hmm the \(n\) is evaluate from 4 to \(n\). 4 is the initial value and \(n\) is the final value.

Answer 19

I am a bad teacher :/

Answer 20

Oh, I'm getting it.

Answer 21

So, it's the sum of values when you substitute n with 4, then 5, then 6, then 7 till n.

Answer 22

Let f(n) be any function or expression.\[\sum_{n=1}^nf(n)\]Then,\[\sum_{n=1}^n f(n)=f(1) + f(2)+\ldots +f(n)\]

Answer 23

Don't say that. I'm a bad learner.

Answer 24

I am getting it... wow, that makes sense!

Answer 25

"So, it's the sum of values when you substitute n with 4, then 5, then 6, then 7 till n."

Yes. Exactly.

Answer 26

it's been discussed to me countless times i still dont get it =_= i never boother nowadays

Answer 27

So, wait, let me try to get the sum of first n natural numbers.

Answer 28

learn about mathematical induction @ParthKohli it's fun :P

Answer 29

For example, \[\sum_{n=1}^nn^2 =1 + 2^2 + 3^2 + \ldots + n^2 \]

Answer 30

Yes, you should learn Mathematical Induction. It's fun. and at times challenging.

Answer 31

Is this the sum of first 4 natural numbers?