# What is an alternating sequence?

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Examples:

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An alternating sequence is a sequence of numbers in which the sign (positive or negative) alternates between consecutive terms. In other words, the terms of the sequence alternate between being greater than and less than zero. For example, the sequence (1, -2, 3, -4, 5, -6, \ldots) is an alternating sequence because the signs alternate between positive and negative.

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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.

- Calc 2 questions super lost! Evaluate a power series to find the sum of the series, or show that the series diverges. (If a series diverges, enter DIVERGES.)? (a) #11/1-11/3+11/5-11/7+11/9-11/11+....# (b)#sum_(n=2)^oo ((-1)^n(8^n))/(n!) #
- How do I write #(5/(1*2))+(5/(2*3))+(5/(3*4))+...+(5/n(n+1))+...#in summation notation, and how can I tell if the series converges?
- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #ln(1/2)+ln(2/3)+ln(3/4)+...+ln(n/(n+1))+...#?
- How do you use the limit comparison test for #sum (2x^4)/(x^5+10)# n=1 to #n=oo#?
- Solve the following (limit; L'Hospital's Rule)?

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