Sequences and Series Cheat Sheet, Lecture notes of Calculus

Download Sequences and Series Cheat Sheet and more Lecture notes Calculus in PDF only on Docsity! Sequences and Series Cheat Sheet 0BArithmetic Sequences and Series 1BGeometric Sequences and Series Arithmetic sequences happen when you add numbers. The number added is called the common difference. Geometric sequences happen when you multiply numbers. The number multiplied is called the common ratio. Recursive formula of an arithmetic sequence: 𝑢𝑛 = 𝑢𝑛−1 + 𝑑 Recursive formula of a geometric sequence: 𝑢𝑛 = 𝑟 ∙ 𝑢𝑛−1 Explicit formula of a basic arithmetic sequence: 𝑢𝑛 = 𝑢1 + (𝑛 − 1)𝑑 𝑜𝑟 𝑢𝑛 = 𝑢𝑜 + 𝑛𝑑 Explicit formula of a basic geometric sequence: 𝑢𝑛 = 𝑢1 ∙ 𝑟𝑛−1 Partial sum of an arithmetic sequence: �𝑢𝑛 = 𝑘 𝑛=1 𝑘 2 (𝑢1 + 𝑢𝑘) 𝑜𝑟 �𝑢𝑛 = 𝑘𝑢1 + 𝑘(𝑘 − 1) 2 𝑑 𝑘 𝑛=1 Partial sum of a geometric sequence: �𝑢𝑛 = 𝑢1 � 1 − 𝑟𝑘 1 − 𝑟 � 𝑘 𝑛=1 To input sums in the (TI-89 and similar) calculator: ∑(𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛, 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒, 𝑏𝑜𝑡𝑡𝑜𝑚 𝑏𝑜𝑢𝑛𝑑, 𝑡𝑜𝑝 𝑏𝑜𝑢𝑛𝑑)