Edexcel A Level Maths: Pure:復(fù)習筆記4.5.1 Language of Sequences & Series
Language of Sequences & Series
What is a sequence?
- A?sequence?is an?ordered?set of numbers with a rule for finding all the numbers in the sequence
- The numbers in a sequence are called?terms
- The terms of a sequence are often referred to by letters with a subscript
What is a series?
- You get a?series?by summing up the terms in a sequence
- We use the notation?Sn?to refer to the sum of the first?n?terms in the seriesie.? ?Sn?=?u1?+?u2?+?u3?+ …?+?un
Increasing, decreasing and periodic sequences
- A sequence is?increasing?if?un+1?>?un?for all positive integers?n?– ie if every term is greater than the term before it
- A sequence is?decreasing?if?un+1?<?un?for all positive integers?n?– ie if every term is less than the term before it
- A sequence is?periodic?if the terms repeat in a cycle
- The?order?(or?period) of a periodic sequence is the number of terms in each repeating cycle
Exam Tip
Look out for sequences defined by trigonometric functions – this can be a way of 'hiding' a periodic function.?
Worked Example
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