Question

How to prove by induction that this is descending?

Answer 1

\[a _{1}=1 \]
\[a _{n+1}=1-\frac{ 1 }{ \sqrt{a _{n}+1} }\]

Answer 2

define 'descending'

Answer 3

I'm having problems with these type of things. How do I prove that this is descending and that the limes is 0. By descending I mean as an grows bigger the numbers get smaller

Answer 4

It's obvious that 1-blabla as \[a_{n}\] grows bigger is getting smaller. I just need to prove it with math induction