Question

Find the limit of the following sequence as \[n\to \infty\]
\[a_n= \left (
\sqrt{n^2 + 10 n} -\sqrt{n^2 + 4 n}\right)
\]
Or say why it diverges.

Answer 1

is it 3 ??

Answer 2

@experimnetX Show the steps.

Answer 3

Rationalizing should work

Answer 4

did exactly same as Ishaan94 said .. multiply both by numerator and denominator ... sqrt(n^2+10n) + sqrt(n^2+4n)

Answer 5

then divide both numerator and denominator by n ---> taking limits we have 6/2 = 3