Geometric sum of a number pattern

Geometric sum of a number pattern

IB Year 5 | Grade 11

Evaluate in terms of \(n\) the sum:

\[3 + 33 + 333 + 3333 + \dots + \underbrace{3 \dots 3}_{n \text{ copies}}\]

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Answer:\(\dfrac13\left[\dfrac{10}{9}(10^n-1)-n\right]\)

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