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nestor18

  • 3 years ago

What does the series converge to? 3/5-9/25+27/125-....... This is a geometric alternating series where A=3/5 and r=3^n/5^n? I think how would I get to its convergence?

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  1. gasgengar
    • 3 years ago
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    The summation of these geometric series to infinity is = a[(1-R^(n+1))/(1-R)] I assume you know how this answer comes from, so a = 3/5, R = (-1) (3/5) and n tends to infinity you'll get the answer = (3/5)/(1+3/5) = 3/8

  2. nestor18
    • 3 years ago
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    I had a brain fart, series was not my strong suit in Calc 2, we barely touched on it.Thanks

  3. cinar
    • 3 years ago
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    \[\Large\sum_{n=1}^{\infty}{(-1)^{n+1}}(\frac{3}{5})^n\]

  4. nestor18
    • 3 years ago
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    I originally put the standard A/1-r and got 15/10, but then I noticed it was an alternating series

  5. cinar
    • 3 years ago
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    answer is 3/8

  6. cinar
    • 3 years ago
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