Question

find the sum of the finite series.
\\(\sum_{n=0}^{17} 12\\)

Explanation:

Step1: Determine the number of terms

The summation is from \( n = 0 \) to \( n = 17 \). To find the number of terms, we use the formula \( \text{Number of terms} = \text{upper limit} - \text{lower limit} + 1 \). So, \( 17 - 0 + 1 = 18 \) terms.

Step2: Calculate the sum

The series is a constant series where each term is 12. The sum of a constant series \( \sum_{n = a}^{b} c \) (where \( c \) is a constant) is given by \( c\times(\text{number of terms}) \). Here, \( c = 12 \) and the number of terms is 18. So, the sum is \( 12\times18 = 216 \).

Answer:

216