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March 29, 2017

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Solve for A and B if:

1 A B
----- = --- + ---
k(k+1) k k+1

  • Pre Calc - ,

    the 1 is over k(k+1), and the A is over k, and the B is over k+1

  • Pre Calc - ,

    common denominator: k(k+1)

    1/[(k)(k+1)]=A(k+1)/[(k)(k+1)] + B(k)/[(k)(k+1)]

    1/[(k)(k+1)]= [ A(k+1)+ B(k)]/ [(k)(k+1)]

    cross multiply:
    [(k)(k+1)]= [ A(k+1)+ B(k)][(k)(k+1)]
    cancel like terms:
    1= [ A(k+1)+ B(k)]
    solve for k!

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