`lim_(nrarroo) ({x}+{2x}+{3x}+...)/n^2`

lim_ (n rarr oo) ({x} + {2x} + {3x} + .... + {nx}) / (n ^ (2))

Evaluate the following limits: lim_(nrarroo)(1^2+2^2+3^2+...+n^2)/n^3

Find the value of the limit lim_(nrarroo)(1^2+2^2+...+n^2)/n^3

lim_(n rarr oo) 5^(((2x)/(x+3)) =

The value of lim_(nrarroo)(cos x cos .(x)/(2)cos.(x)/(4)..cos .(x)/(2^(n))) is equal to

lim_(xrarroo)([x]+[2x]+[3x]+….+[nx])/(n^(2)) , where [*] denotes greatest integer function, is

lim_(nrarroo)([r]+[2r]+ . . . + [nr])/n^2

let lim_ (n rarr oo) ((x ^ (2) + 2x + 3 + sin pi x) ^ (n) -1) / ((x ^ (2) + 2x + 3 + sin pi x) ^ (n ) +1)

Evaluate the limits: lim_(nrarroo)1/n^2(1+2+...+n)

sum_(r=1)^(n)(2r-1)=x" then "lim_(nrarroo)[1^(3)/x^(2)+2^(3)/x^(2)+3^(3)/x^(2)+......+n^(3)/x^(2)]=