# Summation and big theta

Can anyone suggest a starter book or website where I can find information and examples of putting functions under summation signs into Big Theta. basic Arihmetic , geometric, Quadratic are fine , but I would like to work on examples like $$\sum_{i = 1}^{\log n} i \cdot n \text{ or } \sum_{i = 1}^{\log n} 10^i$$

• $\sum_{i=1}^{\log n} i n = n \sum_{i=1}^{\log n} i$ is an arithmetic series (and $n \sum_{i=1}^{\log n} i = \Theta(n \log^2 n)$) . $\sum_{i=1}^{\log n} 10^i$ is a geometric series (and $\sum_{i=1}^{\log n} 10^i = \Theta(n^{\log 10})$). Feb 26 '21 at 11:22