You must assume that . I guess you have already proved that . Call the limit U.Originally Posted by hoeltgman
Now from the definition,
.
Therefore for all n,
.
By induction,
for all n. Now take the limit:
and therefore .
I got two series defined as following:
a and b are positive real numbers.
These two series converge to the same limit. Which I'm supposed to find. I managed to prove that these two series are convergent and even adjacent. But I don't see how to get the limit. All I found out by inserting numbers was that the limit probably is