Let f:N→R be such that f(1)=1 and f(1)+2f(2)+3f(3)+...+nf(n)=n(n+1)f – InterviewSolution

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1.	Let f:N→R be such that f(1)=1 and f(1)+2f(2)+3f(3)+...+nf(n)=n(n+1)f(n), for all n∈N, n≥2, where N is the set of natural numbers and R is the set of real numbers. Then the value of f(500) is
Answer» Let $f : N \to R$ be such that $f (1) = 1$ and $f (1) + 2 f (2) + 3 f (3) + . . . + n f (n) = n (n + 1) f (n)$ , for all $n \in N, n \geq 2,$ where $N$ is the set of natural numbers and $R$ is the set of real numbers. Then the value of $f (500)$ is

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