Question

Please help me find the following limit. (click to see).

Answer 1

\[\lim_{n \rightarrow \infty}\sqrt{n+1}-\sqrt{n+2}\]

Answer 2

there's no denominator ?
you can just plug in n=infinity.

Answer 3

I'm not following

Answer 4

\(\lim_{n \rightarrow \infty}\sqrt{n+1}-\sqrt{n+2}=\sqrt{\infty +1}-\sqrt{\infty+2}=\infty\)

Answer 5

Limits do not work that way. Anyways, the limit is 0.

Answer 6

i am sorry.
did you try L'Hopitals then ?

Answer 7

i mean can you use L
Hopital's rule ?

Answer 8

I could but how do I modify the limit into the form of a fraction.

Answer 9

put x=1/y

Answer 10

sorry, n=1/y

Answer 11

then y->0
n+1 = (1+y )/y

Answer 12

following ?

Answer 13

Try this first:\[(\sqrt{n+1}-\sqrt{n+2})\cdot\frac{\sqrt{n+1}+\sqrt{n+2}}{\sqrt{n+1}+\sqrt{n+2}}\]