Sum of Arithmetic Sequence/Examples
Jump to navigation
Jump to search
Examples of Use of Sum of Arithmetic Sequence
Sum of $j$ from $m$ to $n$
\(\ds \sum_{j \mathop = m}^n j\) | \(=\) | \(\ds m \paren {n - m + 1} + \frac 1 2 \paren {n - m} \paren {n - m + 1}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \frac {n \paren {n + 1} } 2 - \frac {\paren {m - 1} m} 2\) |
Sum of $i + k \paren {2 + 2 i}$
Let $A_n$ be the arithmetic sequence of $n$ terms defined as:
\(\ds A_n\) | \(=\) | \(\ds \sum_{k \mathop = 0}^{n - 1} \paren {a_0 + \paren {2 + 2 i} k}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds i + \paren {2 + 3 i} + \paren {4 + 5 i} + \paren {6 + 7 i} + \dotsb + \paren {2 n - 2 + \paren {2 n - 1} i}\) |
Then:
- $A_n = n \paren {n - 1} + n^2 i$