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    Real analysis

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    Show that if sum(sum sign) to infinity(top) of k=1(bottom) of a_k=A and sum(sum sign) to infinity(top) of k=1(bottom) of b_k=B, then
    1-sum(sum sign) to infinity(top) of k=1(bottom) of ca_k=cA for all c belong to R
    2-sum(sum sign) to infinity(top) of k=1(bottom) of (a_k+b_k)=A+B

    © BrainMass Inc. brainmass.com March 4, 2021, 6:03 pm ad1c9bdddf
    https://brainmass.com/math/real-analysis/real-analysis-summation-26504

    Solution Preview

    1)
    We know that the series converges to A. That means
    lim s_k= lim (a_1 + a_2 + ... + a_k) = A
    k--->infinity

    Now we know from the standard laws of lim that if:

    lim (f(x))= L
    x--->h
    then ...

    Solution Summary

    There are several proofs regarding summations in this solution. The infinite loop function is given.

    $2.19

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