Fix the mistake: Sequences ③ (Sigma and Formulas for Sums)
Sigma Notation Σ
The sum of the sequence {a_k} from k=1 to n is written as
Σ_{k=1}^{n} a_k = a_1 + a_2 + … + a_n .
Linearity:
Σ(α·a_k + β·b_k) = α·Σa_k + β·Σb_k（α, β are constants）
Example ① Calculate Σ_{k=1}^{5} k².
Solution:1+4+9+16+25 = 55
Solution:1+4+9+16+25 = 55
Key Point
- Sigma notation is an “abbreviated notation for addition”
- Constant multiples and sums can be separated
Practice Problem
- Calculate Σ_{k=1}^{4} (2k+1).
Answer and Explanation
- Answer:24
3+5+7+9=24.
Previous and next lessons in this course
- Previous lesson: Fix the mistake: Sequences ② (Geometric Sequences)
- Next lesson: Fix the mistake: Sequences ③ (Sigma and Formulas for Sums)