[2k+1)n^(2)+2(k+3)n+(k+5)=0

lim_ (n rarr oo) sum_ (k = 1) ^ (n) (k + 1) / ((2k + 1) ^ (2) (2k + 3) ^ (2)) equals

lim_ (n rarr oo) sum_ (k = 1) ^ (n) (lambda k ^ (4) + 2k ^ (3) + k ^ (2) + k + 1) / (3n ^ (5) + n ^ (2) + n + 5k) = (1) / (3)

S_(n)=sum_(k=1)^(n)(k^(2)+n^(2))/(n^(3)) and T_(n)=sum_(k=0)^(n-1)(k^(2)+n^(2))/(n^(3)),n in N then

If I_(n) = |(1,k,k),(2n,k^(2) + k + 1,k^(2) + k),(2n -1,k^(2) ,k^(2) + k +1)| and sum_(n=1)^(k) I_(n) = 72 , then k =

2 ^ (k) ([n0]) ([nk]) - 2 ^ (k-1) ([n1]) ([n-1k-1]) + 2 ^ (k-2) ([n2]) ([nk-2]) - ,,, + (- 1) ^ (k) ([nk]) ([nk]) ([n0]) ([n0])

If a_(k)=(1)/(k(k+1)) for k=1,2,3, .. , n, then (sum_(k=1)^(n) a_(k))^(2)=

lim_(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."+n^(2))(1^(3)+2^(3)+"....."+n^(3))) = F(k) , then (k in N)

lim_(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."+n^(2))(1^(3)+2^(3)+"....."+n^(3))) = F(k) , then (k in N)

Statement-1: (C_(0))/(2.3)- (C_(1))/(3.4) +(C_(2))/(4.5)-.............+............+(-1)^(n) (C_(n))/((n+2)(n+3))= (1)/((n+1)(n+2)) Statement-2: (C_(0))/(k)- (C_(1))/(k+1) +(C_(2))/(k+3)+............+(-1)^(n) (C_(n))/(k+n)=int_(0)^(1)x^(k-1) (1 - x)^(n) dx

Statement-1: (C_(0))/(2.3)- (C_(1))/(3.4) +(C_(2))/(4.5)-.............+............+(-1)^(n) (C_(n))/((n+2)(n+3))= (1)/((n+1)(n+2)) Statement-2: (C_(0))/(k)- (C_(1))/(k+1) +(C_(2))/(k+3)+............+(-1)^(n) (C_(n))/(k+n)=int_(0)^(1)x^(k-1) (1 - x)^(n) dx