- #1
Fellowroot
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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.
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(xn) be a sequence of ℝ. The sequence of partial sums (xn) of the series ∑(xn) is defined by sn = ∑xk 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.
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(xn) be a sequence of ℝ. The sequence of partial sums (xn) of the series ∑(xn) is defined by sn = ∑xk 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.