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}ca_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`