The value of the limit when n tends to infinity of the expressionn `n^(1/3)(n^2+1)^(1/3) (2n^2+3n+1)^(-1/2)` is

The value of the limit when n tends to infinity of the expression (1+(1)/(n))^(n) is

The value of the limit when n tends to infinity of the expression,(2n)-:[(2n-1)(3n+5)] is

The value of the limit when n tends to infinity of the expression (n^(4)-7n^(2)+9)-:(3n^(2)+5) is

The value of the limit when n tends to infinity of the expression (7n^(3)-8n^(2)+10n-7)/(8n^(3)-9n^(2)+5) is

The value of the limit when n tends to infinity of the expression 2*(n^(2)+5n+6)[(n+4)(n+5)]^(-1) is

The sum to infinity of the series : 1+2 ( 1-(1)/( n )) + 3( 1 - ( 1)/( n ))^(2) +"...." is :

The sum to infinity of the series 1+2(1-(1)/(n))+3(1-(1)/(n))^(2)+ . . .. . . . , is

If n be a positive integer such that n<=3, then the value of the sum to n terms of the series 1.n-((n-1))/(1!)(n-1)+((n-1)(n-2))/(2!)(n-2)-((n-1)(n-2)(n-3))/(3!)(n-3)+dots