`lim_(n rarr oo)sum_(r=0)^(n)(1/5)^r`

lim_(n rarr oo)(sum_(r=1)^(n)r^(1/a)(n^(a-(1)/(a))+r^(a-(1)/(a))))/(n^(a+1))=

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

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

The value of lim_(n rarr oo)[{4sum_(r=0)^(n)(r+1)(r+2)(r+3)}^((1)/(4))-n] is

If sum_(r=1)^(n)a_(r)=(1)/(6)n(n+1)(n+2) for all n>=1 then lim_(n rarr oo)sum_(r=1)^(n)(1)/(a_(r)) is

The value of lim_(n rarr oo)sum_(r=1)^(n)(1)/(sqrt(n^(2)-r^(2)x^(2))) is

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

If A=([(1)/(2),0-(1)/(3),-(1)/(3)]) then lim_(n rarr oo)sum_(r=1)^(n)r*A^(r-1)

If quad f(x)=lim_(n rarr oo)sum_(r=0)^(n)(tan((x)/(2^(r+1)))+tan^(3)((x)/(2^(r+1))))/(1-tan^(2)((x)/(2^(r+1)))) then lim_(x rarr0)(f(x))/(x) is

lim_(n rarr oo)sum_(i=1)^(n)(5)/(n^(3))(i-1)^(2) equals