Evaluate: `("lim")_(nvecoo)(sumr=1nsqrt(r)sumr=1n1/(sqrt(r)))/(sumr=1n r)`

Evaluate the following limit: lim_(nto oo)(sum_(r=1)^(n) sqrt(r)sum_(r=1)^(h)1/(sqrt(r)))/(sum_(r=1)^(n)r)

Evaluate ("lim")_(nvecoo)sum_(k=1)^nk/(n^2+k^2)

The value of ("lim")_(nvecoo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^2) is equal to 1/(35) (b) 1/4 (c) 1/(10) (d) 1/5

Evaluate: ("lim")_(nvecoo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt(3n^2)))

Evaluate: ("lim")_(nvecoo)((a1 1/x+a2 1/x++a n1/x)/n)^(n x)

If f(x) is integrable over [1,], then int_1^2f(x)dx is equal to ("lim")_(nvecoo)1/nsum_(r=1)^nf(r/n) ("lim")_(nvecoo)1/nsum_(r=n+1)^(2n)f(r/n) ("lim")_(nvecoo)1/nsum_(r=1)^nf((r+n)/n) ("lim")_(nvecoo)1/nsum_(r=1)^(2n)f(r/n)

Evaluate: ("lim")_(n->oo)(-1)^(n-1)sin(pisqrt(n^2+0. 5 n+1)),w h e r en in N

Evaluate: lim_(n->oo)n^2{sqrt((1-cos(1/n))sqrt((1-cos(1/n))sqrt((1-cos(1/n))........oo)))}dot

Evaluate: ("lim")_(nvecoo)n^(-n^2){(n+2^0)(n+2^(-1))(n+2^(-2))(n+2^(-n+1))}^n

Show that ("lim")_(nvecoo)(1/(n+1)+1/(n+2)++1/(6n))=log6