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Math Help - analysis 4.1.3

  1. #1
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    analysis 4.1.3

    how many terms of the series 1-1/2+1/3-1/4+... do we need to take if we are to guarantee that we have an approximation to the target value, ln2, with 10-digit accuracy? with 20-digit accuracy? with 100-digit accuracy?
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  2. #2
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    Quote Originally Posted by pila0688 View Post
    how many terms of the series 1-1/2+1/3-1/4+... do we need to take if we are to guarantee that we have an approximation to the target value, ln2, with 10-digit accuracy? with 20-digit accuracy? with 100-digit accuracy?
    R_N=\left|S-S_n\right|\leq{a_{N+1}}

    Therefore you just need to solve \frac{1}{N+1}\leq{C} where C is the desired accuracy.
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