
sequences Tag Posts Index
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Theorem 2: Series of Sums is equal to Sum of Series
In this video, I go over Theorem 2, which states that we can move a constant out of the sum of a series as well as add or subtract series individually. These follow
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Theorem 2: Series of Sums is equal to Sum of Series
In this video, I go over Theorem 2, which states that we can move a constant out of the sum of a series as well as add or subtract series individually. These follow
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Theorem 1 and the Test for the Divergence of Infinite Series
In this video, I go over Theorem 1, which states that the terms of a convergent series approach zero. Conversely, if the terms don't approach zero, the series diverges,
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Telescoping Sum: All the terms of this series cancel out except for the first and last term
In this video, I go over an infinite series in which arises an example of the famous telescoping sum such that all the terms of the series cancel except for the
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Geometric Series: Sum of x^n series = 1/(1 - x) if |x| is less than 1
In this video, I show that the infinite series xn = x0 + x1 + x2 + ... is just a geometric series, and converges if the absolute value of x is less than 1. By common
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Converting the number 2.3171717... into the fraction 1147/495 via the Geometric Series
In this video, I go over an example of converting the number 2.3171717... (with infinite repeating 17) into a fraction by writing the repeating 17s as an infinite
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Examples on Identifying Geometric Series and Determining if it Converges or Diverges
In this video, I go over two examples and two methods of identifying if a series is a geometric series, and then finding its sum if it converges. In the first example,
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Geometric Series: Deriving the Sum using an Ingenious Method (and via Similar Triangles)
In this video, I go over the geometric series, which is the sum a + a r + a r^2 + ..., and show that if the absolute value of the common ratio r is less than 1,
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Definition and Notation of Infinite Series
In this video, I go over infinite series (or just series), which is defined as the summation of the terms of an infinite sequence of numbers. If we add an infinite
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Definition and Notation of Infinite Series
In this video, I go over infinite series (or just series), which is defined as the summation of the terms of an infinite sequence of numbers. If we add an infinite
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History of the Fibonacci Sequence and the Golden Ratio
In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and
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History of the Fibonacci Sequence and the Golden Ratio
In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and
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Exercise 4: Fibonacci's Original Rabbit Reproduction Sequence (and the Golden Ratio)
In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden
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Exercise 4: Fibonacci's Original Rabbit Reproduction Sequence (and the Golden Ratio)
In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden
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Exercise 3: Convergent Sequence inside a Continuous Function
In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L).
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Exercise 3: Convergent Sequence inside a Continuous Function
In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L).
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Exercise 2: If the limit of the absolute values of a sequence is zero, so is the sequence
In this video I prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved
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Exercise 2: If the limit of the absolute values of a sequence is zero, so is the sequence
In this video I prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved
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Exercise 1: Limit of a Sequence and the Golden Ratio (Minus 1)
In this video I show that the limit of a sequence is the same if the sequence was shifted by 1 term. I use this fact to solve for the limit of a recursive sequence
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Exercise 1: Limit of a Sequence and the Golden Ratio (Minus 1)
In this video I show that the limit of a sequence is the same if the sequence was shifted by 1 term. I use this fact to solve for the limit of a recursive sequence
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