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xEnOnn

  • 4 years ago

How can I know what a summation of series will eventually converge to? For example, in this series: \[\sum _{ i=1 }^{ n }{ { 2 }^{ i-1 } } \] What are the steps I should take to know that it will eventually converge into what equation?

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  1. FoolForMath
    • 4 years ago
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    Hint: This is a geometric series

  2. anonymous
    • 4 years ago
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    another hint, 2>1, so convergence is unlikely

  3. xEnOnn
    • 4 years ago
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    Thanks for the hints. By the way, it does converge. It converges to \[2^n-1\]

  4. xEnOnn
    • 4 years ago
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    But of course, if the series goes to infinity, then it wouldn't converge.

  5. FoolForMath
    • 4 years ago
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    How can a finite series don't converge?

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