This is of the form inf- inf
We can solve it in 2 ways
1) binomial expansion
(n+1)^(1/2) – n ^(1/2) = n^(1/2) + ½(1/n(^(1/2)) + … - n^(/12)
= ½(1/n(^(1/2)) = 0 as n -> inf
2) by rationalising the numerator
(n+1)^(1/2) – n ^(1/2) = ((n+1)^(1/2) – n ^(1/2) ((n+1)^(1/2) + n ^(1/2) / ((n+1)^(1/2) + n ^(1/2)
= 1/(n+1)^(1/2) + n ^(1/2))
= 1/(inf + inf) = 0
The above method shows rationalising the numerator instead of denominator which is generally used can be used as a tool
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