Evaluate `lim_(n->oo) sum r^2/(r^3+n^3)`

Evaluate lim_(n->oo) [sum_(r=1)^n(1/2) ^r] , where [.] denotes the greatest integer function.

Evaluate lim_(n->oo)1/nsum_(r=n+1)^(2n)log_e(1+r/n)

Evaluate lim_(n->oo) [sum_(r=1)^n1/2^r] , where [.] denotes the greatest integer function.

Evaluate lim_(n->oo) [sum_(r=1)^n1/2^r] , where [.] denotes the greatest integer function.

Evaluate: lim_(n rarr oo) (sum_(r=0)^( n) (1)/(2^(r))) .

Evaluate lim_ (n rarr oo) sum_ (r = 2) ^ (n) (n) / ((n + r) ^ (2)) (A) (3) / (4) (B) (2) / ( 3) (C) (2) / (9) (D) (1) / (2)

Evaluate lim _( n to oo) sum_( r =1) ^(n -1) (1)/(sqrt(n ^(2) -r ^(2)))

Evaluate :lim_(n rarr oo)sum_(r=1)^(n)(1)/((n^(2)+r^(2))^(1/2))

Evaluate: lim_(n rarr oo)(sum_(r=1)^(n)sqrt(r)sum_(r=1)^(n)(1)/(sqrt(tau)))/(sum_(r=1)^(n)r)

The value of lim_(n->oo)sum_(r=1)^(n)1/(5^n).^n C_r(sum_(t=0)^(r-1).^r C_t .3^t) is equal to