It appears the mathematical expression given is incomplete or unclear. To provide a detailed, step-by-step solution, I would need more information or a properly formatted mathematical question.
Here are a few things that might be needed for clarification:
- The exact nature of the summation: what are we summing?
- Any missing values or variables: is there a function or a series to consider?
- A proper mathematical context for the problem.
For a typical summation problem, here's an example to illustrate how to approach it:
Suppose we are given the sum of integers from 0 to 20:
[tex]\[
\sum_{i=0}^{20} i
\][/tex]
Step-by-step solution:
1. Identify the first term (a) and the last term (l) of the series. Here, a = 0 and l = 20.
2. Count the number of terms (n) in this series. Since the series includes all integers from 0 to 20, we have [tex]\( n = 20 - 0 + 1 = 21 \)[/tex] terms.
3. Use the formula for the sum of an arithmetic series:
[tex]\[
S_n = \frac{n}{2} (a + l)
\][/tex]
where [tex]\( S_n \)[/tex] is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
4. Plug in the values:
[tex]\[
S_{21} = \frac{21}{2} (0 + 20) = \frac{21}{2} \times 20 = 21 \times 10 = 210
\][/tex]
Thus, the sum of integers from 0 to 20 is 210.
If you can provide additional details or clarify the given expression, I would be happy to help with a more specific and detailed solution.
