If the set of natural numbers is partitioned into subsets `S_1={1},S_2={2,3},S_3={4,5,6}` and so on then find the sum of the terms in `S_(50)dot`

The S.D for the set of the first 'n' natural numbers is

The number of non empty subset of the set {1,2,3,4} is

Find the number of all three elements subsets of the set {a_1, a_2, a_3, a_n} which contain a_3dot

A circle x^2 +y^2 + 4x-2sqrt2 y + c = 0 is the director circle of circle S_1 and S_2 , is the director circle of circle S_1 , and so on. If the sum of radii of all these circles is 2, then find the value of c.

Consider the sequence of natural numbers s_0,s_1,s_2 ,... such that s_0 =3, s_1 = 3 and s_n = 3 + s_(n-1) s_(n-2) , then

An electrical system has open-closed switches S_1, S_2a n dS_3 as shown in fig. The switches operate independently of one another and the current will flow from AtoB either if S_1 is closed or if both S_2a n dS_3 are closed. If P(S_1)=P(S_2)=P(S_3)=1//2, then find the probability that the circuit will work. fig

If S_1 is the sum of an AP of 'n' odd number of terms and S_2 be the sum of the terms of series in odd places of the same AP then S_1/S_2 =

The sum of the squares of three distinct real numbers, which are in GP, is S^(2) . If their sum is a S , then show that a^(2) in ((1)/(3), 1) uu (1,3)

Let S_n denote the sum of first n terms of an A.P. If S_(2n)=3S_n , then find the ratio S_(3n)//S_ndot

Let S_(n) denote the sum of first n terms of an A.P. If S_(4) = -34 , S_(3) = - 60 and S_(6) =- 93 , then the common difference and the first term of the A.P. are respectively.