Hi, I'm trying to proove the following by induction. I think I'm done, but how satisfactory would this proof be for a mathematician?
Thanks for your time.
. If we set it is satisfied, so we suppose it is true for some . Then, for
Hi, I'm trying to proove the following by induction. I think I'm done, but how satisfactory would this proof be for a mathematician?
Thanks for your time.
. If we set it is satisfied, so we suppose it is true for some . Then, for
Suppose
is true. Multiplying through by gives
while multiplying by gives
gives
But
Hence the extra terms on both sides should cancel, giving the result we need.
Important note: Because we assumed the result to be true for both and in order to prove it true for the whole proof by induction should be completed by showing that the result is true for both and (Showing that it is true for just is not good enough.)