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

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

A special die is so constructed that the probabilities of throwing 1, 2, 3, 4, 5 and 6 are (1-k)/(6), (1+2k)/(6), (1-k)/(6), (1+k)/(6), (1-2k)/(6) and (1+k)/(6) , respectively. If two such dice are thrown and the probability of getting a sum equal to 9 lies between (1)/(9) and (2)/(9) , then the integral value of k is

A special die is so constructed that the probabilities of throwing 1, 2, 3, 4, 5 and 6 are (1-k)/(6), (1+2k)/(6), (1-k)/(6), (1+k)/(6), (1-2k)/(6) and (1+k)/(6) , respectively. If two such thrown and the probability of getting a sum equal to lies between (1)/(9) and (2)/(9) , then the integral value of k is

A special die is so constructed that the probabilities of throwing 1, 2, 3, 4, 5 and 6 are (1-k)/(6), (1+2k)/(6), (1-k)/(6), (1+k)/(6), (1-2k)/(6) and (1+k)/(6) , respectively. If two such thrown and the probability of getting a sum equal to lies between (1)/(9) and (2)/(9) , then the integral value of k is

A special die is so constructed that the probabilities of throwing 1, 2, 3, 4, 5 and 6 are (1-k)/(6), (1+2k)/(6), (1-k)/(6), (1+k)/(6), (1-2k)/(6) and (1+k)/(6) , respectively. If two such thrown and the probability of getting a sum equal to lies between (1)/(9) and (2)/(9) , then the integral value of k is

60.A consecutive reaction occurs with two equilibria which co-exist together P(k_(1))/(k_(2) Q (k_(3))/(k_(4) R Where k_(1) , k_(2) , k_(3) and k_(4) are rate constants.Then the equilibrium constant for the reaction P harr R is (1) (k_(1)*k_(2)) / (k_(3)*k_(4) ) (2) (k_(1)*k_(4)) / (k_(2)k_(3) ) (3) k_(1) * k_(2) * k_(3)*k_(4) (4) (k_(1)*k_(3)) / (k_(2)k_(4)) ]]

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

-1=(6k-3)/(k+1)