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Algebra Level 3

A function f(n)f(n), defined for all n∈Nn \in \mathbb N, is such that

f(1)+f(2)+⋯+f(n−1)+f(n)=n2f(n)\large f(1) + f(2) + \cdots + f(n - 1) + f(n) = n^2f(n)

If f(1)=36f(1) = 36, calculate the value of f(8)f(8).

Thành Đạt Lê by Thành Đạt Lê
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