Summation

$\sum_{k = m}^{n} a_{k} = a_{m} + a_{m + 1} + ... + a_{n}$

Summation of arithmetic sequence

For arithmetic sequence $a = a_{k - 1} + d$ : $a_{n} = a_{0} + d_{n}$ $\sum_{k = 0}^{n - 1} a_{k} = \frac{n}{2} (2 a_{0} + (n - 1) d)$

Summation of geometric sequence

For geometric sequence $a_{k} = r a_{k - 1}$ : $a_{n} = a_{0} r^{n}$ $\sum_{k = 0}^{n - 1} a_{k} = a_{0} (\frac{1 - r ^{n}}{1 - r})$

Products

$\prod_{k = m}^{n} a_{k} = a_{m} \cdot a_{m + 1} \cdot ... \cdot a_{n}$

Properties (Theorem 5.1.1)

$\sum_{k = m}^{n} a_{k} + \sum_{k = m}^{n} b_{k} = \sum_{k = m}^{n} (a_{k} + b_{k})$ $c \cdot \sum_{k = m}^{n} a_{k} = \sum_{k = m}^{n} (c \cdot a_{k})$ $\prod_{k = m}^{n} (a_{k} \cdot b_{k}) = (\prod_{k = m}^{n} a_{k}) \cdot (\prod_{k = m}^{n} b_{k})$

🪴 Notes Hehe

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Summations and Products

Summation

Summation of arithmetic sequence

Summation of geometric sequence

Products

Properties (Theorem 5.1.1)

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