Evaluate the Summation sum from k=1 to 17 of 7
Brief Explanation: The problem is asking for the mathematical evaluation of a series where the term to be summed is a constant number 7, and the summation is to be done over a specified range of integer values for the index k. The index k starts at 1 and increases by 1 for each subsequent term, ending when k reaches 17. The summation will involve adding up the constant number 7 a total of 17 times since each value of k from 1 to 17 will contribute a term of 7 to the sum.
$\sum_{k = 1}^{17} 7$
Answer
Solution:
Step 1:
Identify the formula for summing a constant over a range: $\sum_{k = 1}^{n} c = c \cdot n$
Step 2:
Insert the given values into the established formula: $7 \cdot 17$
Step 3:
Calculate the product of $7$ and $17$: $119$
Knowledge Notes:
The problem at hand involves evaluating a summation where the term being summed is a constant. In such cases, the summation simplifies to the product of the constant and the number of terms being summed. The relevant formula is:
$$\sum_{k = 1}^{n} c = c \cdot n$$
where $c$ is the constant value and $n$ is the number of terms.
In this specific problem, the constant is $7$, and the number of terms is $17$ (since we are summing from $k=1$ to $k=17$). By applying the formula, we multiply the constant $7$ by the number of terms $17$ to get the final result.
This process is a straightforward application of the formula for the summation of a constant sequence. It is important to remember that this formula only applies when the terms being summed are constant and do not depend on the variable of summation ($k$ in this case).
