# What is the difference between an infinite sequence and an infinite series?

An infinite sequence of numbers is an ordered list of numbers with an infinite number of numbers.

An infinite series can be thought of as the sum of an infinite sequence.

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An infinite sequence is a list of numbers that continues indefinitely in a specific order, whereas an infinite series is the sum of the terms of an infinite sequence.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you test the improper integral #int 2x(x^2-1)^(-1/3)dx# from #[0,1]# and evaluate if possible?
- Use the Integral Test to determine whether the series is convergent or divergent given #sum 1 / n^5# from n=1 to infinity?
- How do you use the direct Comparison test on the infinite series #sum_(n=1)^oo(1+sin(n))/(5^n)# ?
- Find a series expansion for? : # (1-3x)^(2/3) #
- How do you determine whether the sequence #a_n=(n!)^(1/n)# converges, if so how do you find the limit?

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