summation notation

Summation notation is a compact shorthand for a sum, using the Greek capital letter sigma, Σ. Instead of writing out 1 + 2 + 3 + ... + 100 by hand, you write Σ once and attach instructions telling it what to add.

Below the Σ you put the index and its starting value (like i = 1); above it you put the ending value (like 100); to its right you put the expression for the general term. So the sum of i^2 for i from 1 to n is written as “Σ (from i = 1 to n) of i^2,” which means 1^2 + 2^2 + ... + n^2.

The index letter (i, k, n, ...) is a dummy: it is just a placeholder that marches from the bottom value to the top value, and renaming it changes nothing. A sum from i = 1 to 0 is empty and conventionally equals 0.