Does $1 + 2 + 3 + \cdots+ 2n$ mean the same thing as $\sum\limits_{i=1}^{2n} i$?

Question

Does $1 + 2 + 3 +\cdots + 2n$ mean the same thing as $\displaystyle\sum\limits_{i=1}^{2n} i$?

Answer 1

Yes. $1+2+3+4+...+2n = \displaystyle\sum\limits_{i=1}^{2n} i$

They can in fact be used interchangeably and denote the same sequence and number. One is just the compact form of writing the other.

Refer to this

Answer 2

Yes, it does. That's what a summation is.

Answer 3

Yes. It is, by the definition of summation.