To find the sum of the arithmetic series from 5 to n represented by the sigma notation, we first need to clarify what the series looks like. The expression you’ve provided suggests an arithmetic series where each term increases by a common difference.
Let’s denote the series. The series from 5 up to n can be expressed as:
- 5, 6, 7, …, n
To find the sum of this series, we can use the formula for the sum of an arithmetic series:
S = (n/2) * (first term + last term)
Where:
- S is the sum of the series
- n is the number of terms
- first term is 5
- last term is n
Now, to find n, the number of terms in the series:
Number of terms = (last term – first term) + 1 = (n – 5) + 1 = n – 4
Now, substituting into the sum formula:
S = ((n – 4)/2) * (5 + n)
This gives us the sum of the arithmetic series from 5 to n.
Therefore, the sum of the arithmetic series from 5 to n is:
S = rac{(n – 4)(5 + n)}{2}
In summary, to calculate the sum, substitute the value of n in the formula, and you’ll get the answer based on the limits of your series.