Question

Where's the problem in this solution:

Answer 1

I will prove \[a^{n-1} = 1\] Where a is any non-zero number and n is any natural number, using induction.

Let P(n) be the sentence \[a^{n-1} = 1\]

BASE CASE: P(1):
\[a^{1-1} = a^{0} = 1 \]

INDUCTION:
Suppose P(1), P(2), ...P(n) is all true, I wish to prove P(n+1) is also true.
\[a^{(n+1)-1} = a^n = a^n*\frac{a^{n-2}}{a^{n-2}} = \frac{a^{n-1}*a^{n-1}}{a^{n-2}} = \frac{1*1}{1} = 1\]

Where's the error?

Answer 2

- the denominator of this fraction with a^(n-2) so you need rewriting it in the form of
a^(n-1) *a^(n-1) like in numerator

hope helped