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Given the geometric series $ 15 + 5 + \frac{5}{3} + ...$

  1. Explain why the series converges
  2. Evaluate $ \sum_{n=1}^{\infty} 5(3^{2 - n})$
in Mathematics by Diamond (78,454 points) | 48 views

1 Answer

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1. ratio =5/15 = 1/3 , -1<r<1, hence coverges

2. T1=5(3)=15

T2=5(3)^0=5  , hence the sequence in question 1,

therefore sum to infinity = a/(1-r) = 15/(1- 1/3) =  22.5
by Diamond (44,036 points)

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