Difference between $\sum_{n=1}^{k} f(n)+\sum_{n=1}^{k} g(n)$ and $\sum_{n=1}^{k} [f(n)+g(n)] $ What is difference between $$\sum_{n=1}^{k} f(n)+\sum_{n=1}^{k} g(n)$$ and
$$\sum_{n=1}^{k} [f(n)+g(n)] $$ 

If your $+$ operation is associative (which is the minimum required for operations to make any sense), then there is absolutely no difference.
