What is a Geometric Series?
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A geometric series is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The formula for the nth term of a geometric series is given by (a_n = a_1 \times r^{(n-1)}), where (a_n) is the nth term, (a_1) is the first term, (r) is the common ratio, and (n) is the term number.
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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.
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.
- Does #a_n=(n + (n/2))^(1/n) # converge?
- How do you find the limit of #(e^(3x) - e^(5x))/(x)# as x approaches 0?
- How do you determine whether the sequence #a_n=(-1)^n/sqrtn# converges, if so how do you find the limit?
- How do you find #lim (1/t+1/sqrtt)(sqrt(t+1)-1)# as #t->0^+# using l'Hospital's Rule?
- How do you use the integral test to determine whether #int e^(-x^2)# converges or diverges from #[0,oo)#?

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