I need to prove this result, and although I can see that it is true, I cannot see how to prove it mathematically..rather than just putting in numbers!
sqrt(n+1) - sqrt(n) tends to 0
It depends on how rigorous a proof you require .... A simple approach is to multiply the expression by and simplify. You get and the limiting value is 'obvious' (you could use the sandwich/pinching/squeeze theorem).
Oh ok I see,
That seems to work out very simply, the question says 'give a careful justifcation' so I think that using the squeeze rule as you suggested should be ok! Thank you!