Question

express the following sum in sigma notation. use 1 as the lower limit of summation and k for the index of summation.
4 + 8 + 12 + 16 + 20
express the sum in sigma notation.
20
ς k+
k = 1

Explanation:

Step1: Analyze the pattern

Each term is \(4k\). When \(k = 1\), \(4\times1=4\); when \(k = 2\), \(4\times2 = 8\); when \(k=3\), \(4\times3=12\); when \(k = 4\), \(4\times4=16\); when \(k=5\), \(4\times5 = 20\).

Step2: Write in sigma notation

The sum \(4 + 8+12 + 16+20\) can be written as \(\sum_{k = 1}^{5}4k\)

Answer:

\(\sum_{k = 1}^{5}4k\)