# How you solve this? #lim_(n->oo)sum_(k=1)^n1/((k+1)sqrt(k)+ksqrt(k+1)#

To solve the limit lim_(n->∞) Σ_(k=1)^n 1/((k+1)sqrt(k) + k sqrt(k+1)), you can use telescoping series method. After simplification, you'll find that the terms in the series cancel out, leaving a finite expression which gives the limit. Here's the simplified process:

- Multiply and divide by (sqrt(k+1) - sqrt(k)) to rationalize the denominator.
- Simplify the expression inside the summation to obtain a telescoping series.
- Evaluate the limit as n approaches infinity.

The result should converge to a finite value.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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