Evaluate
`underset(nrarrinfty)Lt(1+2+3+……+n)/(n^2)`.

Evaluate lim_(nrarrinfty)((1)/(2n+1)+(1)/(2n+2)+......+(1)/(6n)) .

underset(nrarrinfty)lim (1^2+2^2+3^2+………+n^2)/n^3 is equal to:

If [x] denotes the greatest integer less than or equal to x, then evaluate underset(ntooo)lim(1)/(n^(2))([1.x]+[2.x]+[3.x]+...+[n.x]).

Evaluate underset(ntooo)limn^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))...(n+2^(-n+1))]^(n) .

The value of lim_(nrarrinfty) ("sin"(pi)/(2n)."sin"(2pi)/(2n)."sin"(3pi)/(2n)..."sin"((n-1)pi)/(2n))^(1/n) is equal to

Find the value underset(n rarr oo)("lim") underset(k =2)overset(n)sum cos^(-1) ((1 + sqrt((k -1) k(k + 1) (k + 2)))/(k(k + 1)))

Evaluate underset(ntooo)limcos(pisqrt(n^(2)+n)) when n is an integer.

Evaluate : underset (r=1) overset (n) sum ""^nC_r 2^r .

Equation x^(n)-1=0,ngt1,ninN, has roots 1,a_(1),a_(2),...,a_(n),. The value of underset(r=2)overset(n)sum(1)/(2-a_(r)), is