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kaykim95

  • 3 years ago

True or false?? This is a convergent geometric series

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  1. kaykim95
    • 3 years ago
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  2. estebananaya
    • 3 years ago
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    i think its convergent, because you can put the argument of the sum like (-3/5)^(i+1) over -5

  3. Lumenaire
    • 3 years ago
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    It is convergent. It's common ratio is -3/5, the absolute value of which is smaller than one. So it does converge.

  4. kaykim95
    • 3 years ago
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    so true?

  5. Lumenaire
    • 3 years ago
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    yes

  6. ZeHanz
    • 3 years ago
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    Rewrite it a little:\[\sum_{i=1}^{\infty}\frac{ 3^{i+1} }{ (-5)^{i+2} }=\sum_{i=1}^{\infty}\frac{ 3^{i+1} }{ (-5)(-5)^{i+1} }=-\frac{ 1 }{ 5 }\sum_{i=1}^{\infty}\left( -\frac{ 3 }{ 5 } \right)^{i+1}\]Now read @Lumenaire 's answer (again)!

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