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Math Help - Inductive Abstract Algebra proofs

  1. #1
    Junior Member
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    Inductive Abstract Algebra proofs

    Prove the 1/(1-x) = 1 + x +x^2 + ... + x^{(n-1)} + x^n/(1-x) for all n greater than or equal to 1.

    Assuming P(n) is the statement above, P(1) is true.
    Induction says that P(n) is true if
    A. P(n0) is true, in this case P(1)
    B. for all k greater than or equal to n0, if P(k) is true then P(k+1) is true.

    However, I can't find a way to show that by assuming P(k) to be true, P(k+1) is therefore also true.
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  2. #2
    Member Black's Avatar
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    1 + x +\cdots+ x^k+ \frac{x^{k+1}}{1-x}=1 + x +\cdots+ \frac{(1-x)x^k}{1-x} + \frac{x^{k+1}}{1-x}=1 + x +\cdots+ \frac{x^k}{1-x}=\frac{1}{1-x}
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