Respuesta :

We need to write the sum in this form:

[tex] \displaystyle \sum_{i=1}^N a_i [/tex]

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

You can easily check that this series is [tex] a_i=2i [/tex]. In fact, you have

[tex]\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}[/tex]

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

So, the sum can be written as

[tex] \displaystyle \sum_{i=1}^{50} 2i [/tex]