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Year 12 Maths Advanced Sequences and Series

Infinite Sum of a GP

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Questions
Question 1
124479

Consider the geometric series \(2+\dfrac{2}{3}+\dfrac{2}{9}+\dfrac{2}{27}+\cdots\)

i) Explain why the series has a limiting sum.

ii) Find the limiting sum.

i) as \(-1<r\left(\dfrac{1}{3}\right)<1\), the series will have a limiting sum.

ii) \(3\)

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