succession limit

[Anakin_99]

Hi guys I'd need some help with this succession limit, first try is right but in the second one the problem is when I put out the n^(n) i guess (where i circled with green). I understood that this is the problem but I can't figure out why cause it seems algebraically correct.
Could u please help me out ? Sorry if my english is so badd.

 

[lex]

Green should be [MATH]n^\frac{1}{n}[/MATH]

 

[Anakin_99]

thank u man

 

[lookagain]

Anakin_99, more connecting steps would help:

\(\displaystyle \sqrt[n]{n + 2 \ } \ =\)

\(\displaystyle \sqrt[n]{n\bigg(1 + \dfrac2n \bigg) } \ = \)

\(\displaystyle \sqrt[n]{n}\sqrt[n]{1 + \tfrac2n} \ =\)

\(\displaystyle n^{1/n}\sqrt[n]{1 + \tfrac2n} \ = \)

 

[Anakin_99]

thank u very much

Anakin_99, more connecting steps would help:

\(\displaystyle \sqrt[n]{n + 2 \ } \ =\)

\(\displaystyle \sqrt[n]{n\bigg(1 + \dfrac2n \bigg) } \ = \)

\(\displaystyle \sqrt[n]{n}\sqrt[n]{1 + \tfrac2n} \ =\)

\(\displaystyle n^{1/n}\sqrt[n]{1 + \tfrac2n} \ = \)

 

[lex]

thank u man

Grand. (I see you marked it solved, so I assume it was all ok).