Find the limit of n(sqrt(n+1) - sqrt(n))^2

  • Thread starter Mattofix
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  • #1
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Homework Statement



Compute lim n-> infinity for xn = n(sqrt(n+1) - sqrt(n))^2

Homework Equations



non (as far as i know)

The Attempt at a Solution



i tried logging it, didnt get me very far though, i had logxn -> log infinty + 2 log sqrt infitity ?????????

pretty stuck...
 

Answers and Replies

  • #2
dynamicsolo
Homework Helper
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Compute lim n-> infinity for xn = n(sqrt(n+1) - sqrt(n))^2

If I'm reading this right, the next thing to do would be to go ahead and multiply out the binomial square to get

(n+1) - { 2 · sqrt(n+1) · sqrt (n) } + n

= (2n + 1) - { 2 · sqrt(n+1) · sqrt (n) } .

This is still an indeterminate difference, but we know what to do with those: multiply by 1 as the ratio of the conjugate factor,

(2n + 1) + { 2 · sqrt(n+1) · sqrt (n) } ,

divided by itself. The numerator simplifies considerably. Now multiply this ratio by the factor n that was originally in front of the squared term in x_n and apply what you know about the limit of a rational function as x approaches infinity.
 
  • #3
138
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thanks :eek:)
 

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