# Math Help - Inductive Abstract Algebra proofs

1. ## 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.

2. $1 + x +\cdots+ x^k+ \frac{x^{k+1}}{1-x}=1 + x +\cdots+ \frac{(1-x)x^k}{1-x} + \frac{x^{k+1}}{1-x}=1 + x +\cdots+ \frac{x^k}{1-x}=\frac{1}{1-x}$