Further Pure Mathematics - 4PM1 PearsonEdexcel

Sigma Notation

Akopọ

Mathematics often requires adding long runs of terms that follow a clear pattern. Sigma notation gives you a compact, precise way to write these sums, replacing pages of repeated addition with a single expression. It is the standard language used across pure mathematics, statistics, and the sciences whenever a sum needs to be communicated without ambiguity.

You will learn to read and interpret sigma expressions, expand them into their individual terms, and convert written-out sums back into sigma form. You will also see how sigma notation connects to arithmetic and geometric series formulas, making evaluation straightforward once you recognise the underlying pattern.

Awọn Afojusun

  1. Use and interpret the sigma notation for summation

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Akọ̀wé Ẹ̀kọ́

Adding the first hundred positive integers by hand would take a while. Writing the sum out in full would fill half a page. Yet the entire instruction can be captured in a few symbols. Sigma notation is that shorthand, and it appears in every branch of mathematics from sequences and series to probability and calculus.

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  1. What does the expression below the sigma symbol represent? A) The upper limit B) The general term C) The starting value of the index D) The sum total Answer: C
  2. How many terms are in the sum from r = 5 to r = 15? A) 10 B) 11 C) 15 D) 20 Answer: B
  3. Evaluate the sum of (2r) from r = 1 to r = 4. A) 8 B) 16 C) 20 D) 24 Answer: C
  4. Which property allows you to write the sum of c times f(r) as c times the sum of f(r)? A) Sum rule B) Constant factor rule C) Splitting rule D) Product rule Answer: B
  5. The sum of the constant 5 from r = 1 to r = 8 equals: A) 5 B) 8 C) 13 D) 40 Answer: D

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