Proving the geometric sum formula by induction
Solution 1:
$$1 - q^{n+1} + q^{n+1}(1-q) = 1 - q^{n+1}(1 - (1-q)) = 1 - (q^{n+1} \cdot q) = \cdots $$
Solution 2:
Did you try expanding the numerator? You have $1-q^{n+1}+q^{n+1}-q^{n+2}$..
Proving the geometric sum formula by induction
Solution 1:
$$1 - q^{n+1} + q^{n+1}(1-q) = 1 - q^{n+1}(1 - (1-q)) = 1 - (q^{n+1} \cdot q) = \cdots $$
Solution 2:
Did you try expanding the numerator? You have $1-q^{n+1}+q^{n+1}-q^{n+2}$..