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    Series S = sin0.2 rad

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    A transcendental irrational number
    S = sin0.2 rad
    can be represented by the infinite series
    S = sum (0 to infinity) of (-1)^n/[5^(2n+1) . (2n+1)!]
    Let its partial sum be
    SN = sum (0 to N) of (-1)^n/[5^(2n+1) . (2n+1)!]

    a) Use the Ratio test to show the series converges absolutely.
    b) Write down explicitly and compute the second (S2) partial sums.
    Hint: in this case, S2 has three terms (using n = 0, 1, 2)
    S2 =
    c) Compute the theoretical error bound of the approximation S ~ S2
    d) Use your computer or calculator to compute the proxy for exact value of sin 0.2. Observe the theoretical error bound holds for S2.
    What does this mean?

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    Solution Summary

    Step-by-step computations and explanations are shown for the questions.