In my book, applied analysis by john hunter it gives me a strange way of stating an infinite sum that I'm still trying to understand because in my calculus books it was never described this way.(adsbygoogle = window.adsbygoogle || []).push({});

It says:

We can use the definition of the convergence of a sequence to define the sum of an infinite series as the limit of its sequence of partial sums. Let(x_{n}) be a sequence of ℝ. The sequence of partial sums (x_{n}) of the series ∑(x_{n}) is defined by s_{n}= ∑x_{k}from k=1 to n.

I just need someone to explain to me how an infinite series is the limit of a sequence of partial sums.

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# Infinite series as the limit of its sequence of partial sums

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