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    Sequences and Limits

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    Consider the real sequence {x_n}_n generated by the iteration scheme

    x_n+1 = x_n(2-ax_n), for n = 0, 1, 2, ......

    where a>0 and x_0 satisfying 0 < x_0 </= 1/a.

    a. Prove 1/a>/=x_n>0 for all n.

    b. Prove x_n>/=x_n-1.

    c. Conclude that lim n-->infinity x_n exists and determine the limit.

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    https://brainmass.com/math/real-analysis/sequences-limits-70413

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    sequence proof
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    Consider the real sequence {x_n}_n generated by the iteration scheme

    x_n+1 = x_n(2-ax_n), ...

    Solution Summary

    Sequences and limits are investigated.

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