OmegaGauss
New member
- Joined
- Aug 25, 2019
- Messages
- 2
So, here's the exercise:
Let fn(x) = x^n +x-1 for n a natural number.
1) Prove that the equation fn(x)=0 has an unique positive solution (called xn)
2)Prove that (xn) converges to 1
3) Give a simple equivalent to (xn-1)
I've already done questions 1 and 2, which weren't all that hard, but the third one is giving me quite some trouble. I've tried finding an equivalent to ln(xn) (by applying ln to the equation), and I've tried to see if any simple function would do the trick, but it didn't seem to work. I then created the series yn=xn-1, and tried manipulating the equation I had, but I haven't gotten anything valuable out of it yet.
Any help would be appreciated!
Let fn(x) = x^n +x-1 for n a natural number.
1) Prove that the equation fn(x)=0 has an unique positive solution (called xn)
2)Prove that (xn) converges to 1
3) Give a simple equivalent to (xn-1)
I've already done questions 1 and 2, which weren't all that hard, but the third one is giving me quite some trouble. I've tried finding an equivalent to ln(xn) (by applying ln to the equation), and I've tried to see if any simple function would do the trick, but it didn't seem to work. I then created the series yn=xn-1, and tried manipulating the equation I had, but I haven't gotten anything valuable out of it yet.
Any help would be appreciated!