`[(k(k+1))/2]^2+(k+1)^3=[((k+1) (k+2))/2 +1]^2`

1+(k)/(3) + (k(k+1))/(3.6) + (k(k+1) (k+2))/(3.6.9) + …=

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

sum_ (k = 1) ^ (n) (2 ^ (k) + 3 ^ (k-1))

Two consecutive irreversible fierst order reactions can be represented by Aoverset(k_(1))(rarr)Boverset(k_(2))(rarr)C The rate equation for A is readily interated to obtain [A]_(t)=[A]_(0).e^(-k_(1^(t))) , and [B]_(t)=(k_(1)[A]_(0))/(k_(2)-k_(1))[e^(-k_(1)(t))-e^(-k_(2)(t))] At what time will B be present in maximum concentration ? a) (K_(1))/(K_(2)-K_(1)) b) (1)/(k_(1)-k_(2) In (k_(1))/(k_(2)) c) (1)/(k_(2)-k_(1)) In (k_(1))/(k_(2)) d) none of these

Lt_(nrarroo) sum_(r=1)^n (2r)^k/n^(k+1),k!=-1 , is equal to (A) 2^k/(k-1) (B) 2^k/k (C) 1/(k+1) (D) 2^k/(k+1)

Lt_(nrarroo) sum_(r=1)^n (2r)^k/n^(k+1),k!=-1 , is equal to (A) 2^k/(k-1) (B) 2^k/k (C) 1/(k+1) (D) 2^k/(k+1)

If (4k _(1), k _(2) ^(2) , 1) and ( 4k _(2) , k _(2) ^(2), 1) are two points lying on the plane in which (2,3,2) and (1,2,1) are mirror image to each other, then k _(1) k _(2) is equal to

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)