Quote:
Originally Posted by Kat-M  here is the correct problem. In the original question i had 1+x(n)/(1+x(n+1)) but it should be 1+x(n)/(1+x(n)).
suppose {x(n)} is a sequence such that
x(1)=1 and
x(n+1)=1+x(n)/(1+x(n)) ; n>=1
Prove that this sequence converges and find the limit.
I know how to find the limit of this sequence but dont know how to show that {x(n)} is a convergent sequence. Please help me on this. |
Another way is to solve your problem directly. The substitution
for suitable
(guess what number see HallsofIvy reply) the difference equation will become a linear difference equation which can be solved exactly.