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OK, I've tried solving the question, and here's what I've been able to do so far:
But I'm lost here.
What do I do now?
Subtract both equations and we get
which gives a recurrance equation.
Hint : what is $n^2f(n)-(n-1)^2f(n-1)$ ?
In a more general case, when you have this kind of summations, always try to simplify terms. It can help.
As suggested by @Vincent, we have
Required, but never shown