Evalu0k Lorn njm2 Solutionwe can write it as k1n 1nsqrtnnk

Solution

we can write it as

_k=1..n 1/n*sqrt(n/(n+k))

=_k=1..n 1/n*sqrt(1/(1+k/n))

We recognize this as a Riemann sum from 0 to 1 with intervals of length 1/n

So the limit is equal to

₀¹sqrt(1/(x+1)) dx

=2sqrt(x+1)|₀¹

=2(2-1)