Question

use the following image to answer the question.
question 43
which series is represented by the summation notation given?
select one
\\(\sum\limits_{j=1}^{5} 2j\\)
\\(\bigcirc\\) 2+4+6+8+10
\\(\bigcirc\\) 1+2+3+4+5
\\(\bigcirc\\) 2+6+8+10
\\(\bigcirc\\) 1+3+5

Explanation:

Step1: Understand Summation Notation

The summation $\sum_{j = 1}^{5}2j$ means we substitute $j = 1,2,3,4,5$ into $2j$ and sum the results.

Step2: Calculate Each Term

• For $j = 1$: $2\times1 = 2$
• For $j = 2$: $2\times2 = 4$
• For $j = 3$: $2\times3 = 6$
• For $j = 4$: $2\times4 = 8$
• For $j = 5$: $2\times5 = 10$

Step3: Form the Series

Summing these terms gives $2 + 4 + 6 + 8 + 10$.

Answer:

A. $2 + 4 + 6 + 8 + 10$