Science:Math Exam Resources/Courses/MATH101/April 2014/Question 07 (a)/Hint 2

Notice if we take $n$ to be large then

${\frac {1}{\sqrt {n^{2}+1}}}\approx {\frac {1}{\sqrt {n^{2}}}}={\frac {1}{n}}.$

What is the convergence behaviour of ${\frac {1}{n}}$? This should give us a hint of what kind of series we should try and compare to.