Question

Write the series 2+4+6+8+...+100 in sigma notation

Answer 1

We need to write the sum in this form:

$\displaystyle \sum_{i=1}^N a_i$

So, we need to find an appropriate sequence, such that $a_i$ is the i-th even number.

You can easily check that this series is $a_i=2i$. In fact, you have

$\begin{array}{c|c|c}a_1&2\cdot 1&2\\a_2&2\cdot 2&4\\a_3&2\cdot 3&6\\a_4&2\cdot4&8\end{array}$

and so on. Finally, we have to observe that we want the first 50 elements of this sequence, since $a_{50} = 2\cdot 50 = 100$.

So, the sum can be written as

$\displaystyle \sum_{i=1}^{50} 2i$