# Fuzzy Operators

**Computer Science**Level 4

\[ S_n = 1 + 2 - 3 \times 4\div 5 + 6 - 7 \times 8 \div 9 +10- \cdots n \]

Consider the above sum where the first \(n\) positive integers are listed in ascending order, and the mathematical operations \((+,-,\times,\div)\) are repeated in that order.

Find the value of \(S_{31417} \). Give your answer to 3 decimal places.

**Details and Assumptions**:

BODMAS (Order of Operations) is obeyed.

A couple of explicit examples: \(\begin{align} S_4 &= 1 + 2 - 3\times4 = (1+2) - (3\times4) = 3 - 12=-9 \\ S_5 &= 1+2-3\times4\div5 = (1+2) - (3\times4\div5) = 3 - 12\div5 = 0.6. \end{align} \)

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