Question:medium
For all real numbers \( x \) and \( y \), it is known that the real valued function \( f \) satisfies \( f(x) + f(y) = f(x + y) \). If \( f(1) = 7 \), then \( \sum_{r=1}^{100} f(r) \) is equal to:
For all real numbers \( x \) and \( y \), it is known that the real valued function \( f \) satisfies \( f(x) + f(y) = f(x + y) \). If \( f(1) = 7 \), then \( \sum_{r=1}^{100} f(r) \) is equal to:
Show Hint
Cauchy's equation implies linearity. If you know \( f(1) \), then \( f(n) = n \cdot f(1) \). The sum then becomes \( f(1) \cdot \frac{n(n+1)}{2} \).
Updated On: May 1, 2026
- \( 7 \times 51 \times 102 \)
- \( 6 \times 50 \times 102 \)
- \( 7 \times 50 \times 102 \)
- \( 6 \times 25 \times 102 \)
- \( 7 \times 50 \times 101 \)
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The Correct Option is
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