An= square root (n+ square root n + 1) - n find limit of sequence.

my work: lim as x goes to infinite x(1+ (x+1)^ 1/2 / (x))^ (1/2) - squareroot x

i think the limit is infinite minus infinite but how do i change it into the indeterminate form.

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- Mar 17th 2009, 08:10 PMtwilightstrfind limit of sequence
An= square root (n+ square root n + 1) - n find limit of sequence.

my work: lim as x goes to infinite x(1+ (x+1)^ 1/2 / (x))^ (1/2) - squareroot x

i think the limit is infinite minus infinite but how do i change it into the indeterminate form. - Mar 17th 2009, 08:18 PMGaloisTheory1
- Mar 17th 2009, 09:11 PMtwilightstr
the problem is square root of n + squareroot of n+1)) - square root of n

everything before square root n is within a square root - Mar 17th 2009, 09:37 PMChris L T521
Thus, $\displaystyle \lim\left(\sqrt{n+\sqrt{n+1}}-\sqrt{n}\right)\frac{\sqrt{n+\sqrt{n+1}}+\sqrt{n}} {\sqrt{n+\sqrt{n+1}}+\sqrt{n}}=\lim\frac{\sqrt{n+1 }}{\sqrt{n+\sqrt{n+1}}+\sqrt{n}}$ $\displaystyle =\lim\frac{1}{\sqrt{\frac{n}{n+1}+\frac{1}{\sqrt{n +1}}}+\sqrt{\frac{n}{n+1}}}=\boxed{\frac{1}{2}}$

Does this make sense? - Mar 19th 2009, 07:47 PMtwilightstr
what happened after the second to last step?

- Mar 20th 2009, 04:01 AMstapel