Introduction to Sequences and Series: Fundamentals, Types, and Applications
Here are a few examples to illustrate sequences and series: Arithmetic Sequence: \(2, 5, 8, 11, \ldots\), where each term increases by a constant difference of \(3\). Arithmetic Series: Summing the terms of an arithmetic sequence, like \(2 + 5 + 8 + 11 + \ldots\). Its sum can be found using \(\frac{n}{2} \times (\text{first […]
Types of Sequences and Series: Key Concepts with Practical Examples
Sequences and series come in various types. Arithmetic sequences have a constant difference between terms, while geometric sequences have a constant ratio. Harmonic sequences involve the reciprocals of integers, while Fibonacci sequences add the previous two terms. Series, the sum of sequence terms, follow similar classifications: arithmetic series, geometric series, and harmonic series. Convergence is […]
