Sigma symbol of mathematical knowledge

Since I have never been very good at mathematics, I plan to learn new things and make a record. Today I have come into contact with this mathematical symbol, and I have never been familiar with it before. Today I will make a summary, for future use.

Hexan ID (Transliteration: sigma)

Sign of summation is first used by Euler (1707-1783) in 1755. This symbol is

Because of the Greek (ADD) header, "Sigma" is the capital of σ.

Example: Σ an = A1 + A2 +... +

Σ is the short mark of the sum of the series. K ^ 2 is the general formula behind it. k = 1 below is the number of items starting from the initial item, and N on the top is the number of last items.

.
N
Σ K ^ 2 = 1 ^ 2 + 2 ^ 2 + ...... + N ^ 2 ...... (1)
K = 1
N
Σ (2 k + 1) = 3 + 5 + ...... + (2n + 1 )...... (2)
K = 1
Then (1) + (2) =
N
Σ (k + 1) ^ 2 = 2 ^ 2 + 3 ^ 2 + ...... + (N + 1) ^ 2
K = 1
The expansion of the famous binary theorem can be expressed
N
Σ C (n, k) A ^ (n-k) B ^ K.
K = 0
It can be seen that the application is quite flexible.