Σ 与 Π 记号

Introduction: Compact Summation Notation

Definition of Summation Notation

What is the value of $\sum_{k=1}^{4} k^2$?

Linearity

What is $\sum_{k=1}^{n} 3a_k$ equal to?

The Telescoping Method

What is $\sum_{k=1}^{n}(a_{k+1} - a_k)$ equal to?

Product Notation and Factorial

What is $5!$?

Worked Example: Key Summation Formulas

Compute $\sum_{k=1}^{10} k^2 = 1^2 + 2^2 + \cdots + 10^2$. Enter an integer.

Compute $\sum_{k=0}^{4} 2^k = 1 + 2 + 4 + 8 + 16$. Enter an integer.

Compute $\sum_{k=1}^{5}\left(\dfrac{1}{k}-\dfrac{1}{k+1}\right)$; enter the integer numerator $a$ of the resulting fraction $\dfrac{a}{b}$.

What are the three key summation formulas?

In your own words, explain why the summation index can be renamed (dummy index). What must be kept in mind when reindexing?

Comprehensive Check

Lesson Summary