# How to understand sum symbol?

I have searched google for an answer but I'm not sure what I'm asking. I know that Sigma means sum but there is an 'n' above Sigma and an 'i=1' under sigma. how can i understand this? thank you!

• Shorthand notation for "$a_1+a_2+\cdots+ a_n$" is "$\sum\limits_{i=1}^n a_i$". You would read that summation symbol as "the sum from $i=1$ to $n$ of $a_i$". – David Mitra Aug 27 '13 at 15:16
• Ok so it's just a counting sequence! – Hermes Trismegistus Aug 27 '13 at 15:18
• @DavidMitra I know what you mean, but just so this doesn't go without saying, it's $a_1+a_2+\ldots +a_n$ that is short for $\sum \limits_{i=1}^na_n$. – Git Gud Aug 27 '13 at 15:20
• @GitGud You do realize $a_1+\cdots+a_n$ is really "informal" notation for an otherwise well defined and compact $\sum_{i=1}^n a_i$? – Pedro Tamaroff Aug 28 '13 at 3:10
• @PeterTamaroff That's exactly what my comment above conveys. – Git Gud Aug 28 '13 at 9:04

$\sum_{i=m}^n a_i = a_m + a_{m+1} + a_{m+2} +\cdots+ a_{n-1} + a_n.$