Could someone help me with setting up a problem . So i want to prove something by induction on k = 0,1,2,3,4...n, clearly
I have two functions: g(x) and f(x) and i have observed that
so it looks like :
and if i check that for all k up to 100 i get correct numbers.
And as I said i would like to prove this ( ) by induction on k So my question is what is my base case and what my induction hypothesis? To me it looks like my base case is :
and my induction H:
but what confuses me is if if i plug in 0 for k here i get :
which is not y which means that either i have wrong idea about my base case (although i always recieve f(0) = g(0)) or my induction hypothesis is wrong (but for all k > 0 i always get the right numbers if i apply ). I don't know how to connect these two together.
One more information . This ofcourse works if y = 0 but y = 1,2,3..n so and