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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