Thread: Induction Problem

having problems with the following problem:

Consider,




Use the principle of induction to prove that for n>=1 the derivative of is:

if anyone could show me how to solve this problem it would be much appreciated.

Originally Posted by Jonny-123

having problems with the following problem:

Consider,




Use the principle of induction to prove that for n>=1 the derivative of is:

if anyone could show me how to solve this problem it would be much appreciated.

note that

First verify the base case when n=1



So the base case checks

Now we assume it is true for n and show n+1



Now take the derivative of the induction hypothsis to get



lets simplify a bit



and now factor out a 2 to get





but this isn't quite what we want so lets build the fraction by multiplying by (n+1)









and we are done.