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Introduction to Series Video Lecture | Algebra - Mathematics
FAQs on Introduction to Series Video Lecture - Algebra - Mathematics
| 1. What is a series in mathematics? |  |
A series in mathematics is the sum of the terms of a sequence. It is a way to add up an infinite number of terms or a finite number of terms in a specific order. The terms of a series can be positive, negative, or zero, and they can follow a pattern or be completely random.
| 2. What is the difference between an arithmetic series and a geometric series? | |
An arithmetic series is a series in which each term is obtained by adding a constant difference to the previous term. In other words, the terms of an arithmetic series form an arithmetic progression.
On the other hand, a geometric series is a series in which each term is obtained by multiplying the previous term by a constant ratio. In other words, the terms of a geometric series form a geometric progression.
| 3. How can I determine the sum of an arithmetic series? | |
To determine the sum of an arithmetic series, you can use the formula:
S = (n/2)(a + l),
where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
Alternatively, you can use the formula:
S = (n/2)(2a + (n-1)d),
where d is the common difference between the terms.
| 4. How can I determine the sum of a geometric series? | |
To determine the sum of a geometric series, you can use the formula:
S = a(1 - r^n) / (1 - r),
where S is the sum of the series, a is the first term, r is the common ratio between the terms, and n is the number of terms.
If the common ratio r is between -1 and 1, and the number of terms n approaches infinity, you can use the formula:
S = a / (1 - r).
| 5. Can a series have an infinite sum? | |
Yes, a series can have an infinite sum. This means that the sum of its terms goes to infinity as the number of terms increases. An example of an infinite series is the harmonic series:
1 + 1/2 + 1/3 + 1/4 + ...
However, not all series have an infinite sum. Some series have a finite sum, meaning that the sum of their terms is a specific number.
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