Let Un be the sequence such that U(n+1)=ln(1+Un)
Let Vn be the sequence such that Vn=1/U(n+1)−1/Un.
Hello, I am stuck on the question: Find the limit of Vn. I thought about defining a function f such that f(x)=ln(1+x) and then studying it (as I did to find the limit of the sequence Un). However, I am doubtful about this because it doesn't seem to be a sequence defined by recurrence. The limit using this method would be 0.5, which is correct according to some checks with the calculator. Could you explain to me why this works and if there is another method that I am unaware of?
Thank you
Let Vn be the sequence such that Vn=1/U(n+1)−1/Un.
Hello, I am stuck on the question: Find the limit of Vn. I thought about defining a function f such that f(x)=ln(1+x) and then studying it (as I did to find the limit of the sequence Un). However, I am doubtful about this because it doesn't seem to be a sequence defined by recurrence. The limit using this method would be 0.5, which is correct according to some checks with the calculator. Could you explain to me why this works and if there is another method that I am unaware of?
Thank you