Your common denominator is incorrect. It should be just
Hi, i've been solving some excersices but I am stuck with this one.
Proof by Mathematical Induction the following expresion
Well the first thing I did was rewrite the expesion as this:
then i proof this is true for p(1)
then I assume this true for p(k)
p(k+1)
then
replacing S_{k}
and then i did the sum
after this step I don't really know what to do for symplify the expression, so if can help it would be great and if i made a mistake in previous steps please make know. thanks
For those who will be visiting this thread in the future this is the whole answer to the problem
#Problem
Proof by mathematical induction the following expression
At first place to do this more easy to understand we rewrite this expression like:
and then we will proof this is true for P(1)
then we will assume this is true for P(k)
and then we will proof thi is true for P(k+1)
then we must obtain that S_{k+1} is equal to the sum of S_{k} and U_{k+1}
replacing S_{k}
and doing the sum and keeping the common denominator as (k+3)! we obtain this
then we know that
the answer continues on the next post