Explore BrainMass
Share

Explore BrainMass

    Series S = sin0.2 rad

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?

    © BrainMass Inc. brainmass.com October 10, 2019, 8:12 am ad1c9bdddf
    https://brainmass.com/math/basic-calculus/613265

    Attachments

    Solution Summary

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

    $2.19