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Dido525

  • 3 years ago

Find the limit \[\lim_{n \rightarrow \infty} \frac{ 1 }{ n } \sum_{i=1}^{n} \frac{ 1 }{ 1+(\frac{ i }{ n })^2 }\]

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  1. Dido525
    • 3 years ago
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    I got: \[\frac{ \pi }{ 4 }\]

  2. Dido525
    • 3 years ago
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    Is that right?

  3. Dido525
    • 3 years ago
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    \[\lim_{n \rightarrow \infty} \frac{ 1 }{ n } \sum_{i=1}^{n} \frac{ 1 }{ 1+(\frac{ i }{ n })^2 }\]

  4. experimentX
    • 3 years ago
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    yes you are right .. change it into integration

  5. Dido525
    • 3 years ago
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    Thanks :) .

  6. experimentX
    • 3 years ago
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    this should be equal to \[ \int_0^1 {1 \over 1 + x^2} dx\]

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