Sigma Notation

${\Sigma }_k^{n}f(x)$ A condensed way of writing a series Example: ${\Sigma }_{k=3}^{12}2k^2=2(3{)}^2+2(4{)}^2\dots 2(12{)}^2$

Definition

${\sum }_{k=m}^n{a}_k=(a_m+a_{m+1}+\cdots +a_{n-1}+a_n)$

Anatomy

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Text Elements

general term

k = m

e

a

k

start index

index

end index

Link to original

• $k$ is the index
• $m$ is the non-negative starting index
• $e$ is the non-negative end index
• $e>m$

Properties of Sigma Notation

Sum/Diff

${\sum }_{k=1}^n(a_k+b_k)={\sum }_{k=1}^n(a_k)+{\sum }_{k=1}^n(b_k)$

Constant Multiple

${\sum }_{k=1}^{n}c(a_k)=c{\sum }_{k=1}^n(a_k)$

Splitting Sum

${\sum }_{k=1}^n(a_k)={\sum }_{k=1}^{l-1}(a_k)+{\sum }_{k=l}^n(a_k)$ Where $1<l\le n$

Sigma Notations For Series

• Sum of Constant Series
• Sum of Linear Series
• Sum of Quadratic Series
• Sum of Cubic Series
• Sum of Exponential Series