# Be a little Gauss

Algebra Level 2

When Gauss was a little boy, he demonstrated how to sum up all the integers from 1 to 100 as follows:

He wrote the numbers down in ascending order. Then, beneath these numbers, he wrote them down again in descending order. As such, the sum in each column is the same, namely $$101$$.

$\begin{array} { l l l l l l l l l l l l l l } 1 & + 2 & + 3 & + 4 & \ldots & + 100 \\ 100 & + 99 & + 98 & + 97 & \ldots & + 1 \\ \hline 101 & + 101 & + 101 & +101 & \ldots & + 101 \\ \end{array}$

Since twice of the sum is equal to $$101 \times 100$$, hence the sum is $$\frac{101 \times 100 } { 2} = 5050$$.

Learning from this approach, what is the sum of all positive multiples of 5 that are strictly less than 100?

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