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Example of GP: choice of formulae

Example of GP: choice of formulae

IB Year 5 | Grade 11

Now ,in practice when we apply this formula, we have a choice to make when we perform the actual calculations. Let us use an example to illustrate.

Find the sum of the first \(n\) terms of the geometric series:

  1. \(2-6+18-\dots\)
  2. \(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\dots\)

Solution:

Solution locked

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Answer:(a) \(S_n=\dfrac{1-(-3)^n}2\) (b) \(S_n=\dfrac32\left(1-\dfrac1{3^n}\right)\)

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