Mathematics (AS)·Sequences and series · NSSCAS 1.2.4
Sigma notation & the sum to infinity
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That big Greek letter Σ is not scary — it is just a neat way of saying 'add these up'. In this lesson you will learn to read sigma notation out loud, expand it term by term, and write your own. Then comes the magic: adding infinitely many numbers and getting one tidy answer, using the condition |r| < 1 and the formula S∞ = a/(1 − r). We even turn a never-ending decimal into an exact fraction — a real exam favourite.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.2.4):
- Interpret and apply the Sigma (Σ) notation.
- Use the condition for the convergence of a geometric progression (|r| < 1).
- Use the formula for the sum to infinity of a convergent geometric progression, S∞ = a/(1 − r).
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Miss Eve and Mike talk through the whole topic — with the figure and working drawn live.