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- Homework Statement
- Find limit an n-> infinity (n*sqrt(n)) / (n+1)sqrt(n+1))

- Relevant Equations
- L'Hopital's rule f'(n) / g'(n)

Hello,

This is actually a piece of a little bigger problem (convergence of a series) - you can see the ratio test ak+1 / ak

That's why the (n) and (n+1) terms

I have lim n->∞ of (n√n) / (n+1)√(n+1) ∞/∞

I have tried L'Hopitals rule (requiring multiple times) and I am not seeing an end.

derivative of n^3/2/ (n(n+1)^1/2 + (n+1)^1/2)

lim 3/2 n^1/2 / (1)( n+1)^1/2 + (n)1/2(n+1)^(-1/2) + (1/2 (n+1)^(-1/2) )

form is still ∞/∞

Looking ahead ... it looks as if continuing to apply L'Hopitals rule because of the fractional exponents I will be stuck in a repetitive always getting ∞/∞

The answer (just the answer) was provided to this problem, the series does converge (within a bound) so I know this limit is not ∞/∞

Am I on the right track with L'Hopitals Rule or am I overlooking some simplification to make things easier?

Thanks

Sparky_

This is actually a piece of a little bigger problem (convergence of a series) - you can see the ratio test ak+1 / ak

That's why the (n) and (n+1) terms

I have lim n->∞ of (n√n) / (n+1)√(n+1) ∞/∞

I have tried L'Hopitals rule (requiring multiple times) and I am not seeing an end.

derivative of n^3/2/ (n(n+1)^1/2 + (n+1)^1/2)

lim 3/2 n^1/2 / (1)( n+1)^1/2 + (n)1/2(n+1)^(-1/2) + (1/2 (n+1)^(-1/2) )

form is still ∞/∞

Looking ahead ... it looks as if continuing to apply L'Hopitals rule because of the fractional exponents I will be stuck in a repetitive always getting ∞/∞

The answer (just the answer) was provided to this problem, the series does converge (within a bound) so I know this limit is not ∞/∞

Am I on the right track with L'Hopitals Rule or am I overlooking some simplification to make things easier?

Thanks

Sparky_

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