if a>0 and
and
find the limit of the sequence as n goes to infinity
Thank you, but i am not so sure why we must take the positive sqrt of a as the limit of the function because all the terms of the sequence are positive .Is there a theorem or another problem ,saying that if all the terms of the sequence are +ve then the limit of the function must be +ve??
To prove convergence i tried hard with no result so a complete proof will be very mush appreciated it
By considering the difference :
we can study the monotony of the sequence .
But in this difference all terms are positive except the term which can be positive or -ve for all values of nεN.
At the same time if we can prove whether the term is +ve or -ve we will have proved whether the sequence is bounded above or bellow by sqrt(a).
So how do we that ,if anyone knows please help.