`([n],[0])+2([n],[1])+2^(2)([n],[2])+........+2^(n)([n],[n])` is equal to

lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n)is equal to

If n=5 ,then ("^n C_0)^(2) + ("^n C_1)^(2) + ("^n C_2)^(2) +......+ ("^n C_5)^(2) is equal to

lim_(n rarr oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2)) + (n)/(n^(2)+3^(2))+......+(1)/(5n)) is equal to :

If S_(n)=sum_(r=1)^(n)(1+2+2^(2)+......+2^(r))/(2^(r)), then S_(n) is equal to (a)2^(n)n-1( b) 1-(1)/(2^(n))(c)2n-1+(1)/(2^(n))(d)2^(n)-1

lim_(n to oo ) {(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+ (n)/(n^(2)+n^(2))} is equal to

The value of (nC_(0))/(n)+(nC_(1))/(n+1)+(nC_(2))/(n+2)+......+(nC_(n))/(2n) is equal to

The value of hat r(2n+1)C_(0)^(2)+^(2n+1)C_(1)^(2)+^(2n+1)C_(2)^(2)+....+^(2n+1)C_(n)^(2) is equal to

If n in N then hat sim(n)C_(0)+^(n+1)C_(1)+^(n+2)C_(2)+....+^(n+r)C_(i) is equal to