Let be such that and f(1) + 2f(2) + 3f(3) + + nf(n) = n(n+1)f(n)

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

f: \mathbb{N} \to \mathbb{R}

be such that

f(1) = 1

and

f(1) + 2f(2) + 3f(3) + \dots + nf(n) = n(n+1)f(n), \text{ for } n \ge 2

\text{then } \frac{1}{2010 f(2010)} \text{ is } \dots\dots\dots\dots\dots