Given a continuous function f(x) in the interval [a,b] , I need to prove that
I think I should do it somehow through Riemann's Integral defnition and/or use Riemann's sums , but I tried to play with it for a while and I haven't gotten anywhere....
Any ideas how should I start proving this?
Thanks in advance!
In my task , after this question, I need to calculate a few limits using the formula
I managed to calculate all the limits in the task except of this limit
I tried many times but I couldn't write this expression as a sum of f(k/n)...
The problem is what's inside the ln function , i.e 2n+1 , 2n+2 , ... , 2n+k , can't be written as an expression of k/n , so I am kinda stuck....
Any ideas people ?