Given, f(1) = 1 and n × f(x) = f(nx), then f(1) + f(2) + f(3) + … + f(100) =
Explanation:
Given, f(1) = 1 and f(nx) = n × f(x)
Putting n = 2 and x = 1, we get f(2) = 2 × f(1) = 2
Putting n = 3 and x = 1, we get f(3) = 3 × f(1) = 3
…
Putting n = 100 and x = 1, we get f(100) = 100 × f(1) = 100.
∴ f(1) + f(2) + f(3) + … + f(100) = 1 + 2 +3 + … + 100 = 5050.
Hence, option (c).
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