Question

For every natural number f:N→R satisfies the condition that f(1)+f(2)+⋯+f(n)=n^2∙f(n).If f(1)=2014 , then determine f(2013).

Answer 1

i think
\[f(2013) = \frac{(2012^2 * 2011^2 * 2010^2 * ... * 1^2)f(1)}{(2013^2-1)(2012^2-1)(2010^2-1) ...(2^2-1)}\]