Let P be a product given by `P = (x+a_1)(x + a_2) ....... (x + a_n)` and Let `S_1= a_1+ a_2+......+a_n=sum_(i=1)^na_i,S_2sum sum _(i lt j) a_i.a_j,S_3=sum sum_(i lt j lt k)` , and so onow that then it can be show that `P=x^n+S_1x^(n-1)+S_2x^(n-2)+..........+S_n`. The coefficient of `x^8` in the expression `(2 + x)^2(3 + x)^3 (4 + x)^4` must be (A)26 (B)27 (C)28 (D)29

If (x + a_(1)) (x + a_(2)) (x + a_(3)) …(x + a_(n)) = x^(n) + S_(1) x^(n-1) + S_(2) x^(n-2) + …+ S_(n) where , S_(1) = sum_(i=0)^(n) a_(i), S_(2) = (sumsum)_(1lei lt j le n) a_(i) a_(j) , S_(3) (sumsumsum)_(1le i ltk le n)a_(i) a_(j) a_(k) and so on . Coefficient of x^(7) in the expansion of (1 + x)^(2) (3 + x)^(3) (5 + x)^(4) is

If (x + a_(1)) (x + a_(2)) (x + a_(3)) …(x + a_(n)) = x^(n) + S_(1) x^(n-1) + S_(2) x^(n-2) + …+ S_(n) where , S_(1) = sum_(i=0)^(n) a_(i), S_(2) = (sumsum)_(1lei lt j le n) a_(i) a_(j) , S_(3) (sumsumsum)_(1le i ltk le n)a_(i) a_(j) a_(k) and so on . Coefficient of x^(7) in the expansion of (1 + x)^(2) (3 + x)^(3) (5 + x)^(4) is

If (x + a_(1)) (x + a_(2)) (x + a_(3)) …(x + a_(n)) = x^(n) + S_(1) x^(n-1) + S_(2) x^(n-2) + …+ S_(n) where , S_(1) = sum_(i=0)^(n) a_(i), S_(2) = (sumsum)_(1lei lt j le n) a_(i) a_(j) , S_(3) (sumsumsum)_(1le i ltk le n)a_(i) a_(j) a_(k) and so on . Coefficient of x^(7) in the expansion of (1 + x)^(2) (3 + x)^(3) (5 + x)^(4) is

If (x + a_(1)) (x + a_(2)) (x + a_(3)) …(x + a_(n)) = x^(n) + S_(1) x^(n-1) + S_(2) x^(n-2) + …+ S_(n) where , S_(1) = sum_(i=0)^(n) a_(i), S_(2) = (sumsum)_(1lei lt j le n) a_(i) a_(j) , S_(3) (sumsumsum)_(1le i ltk le n) a_(i) a_(j) a_(k) and so on . If (1 + x)^(n) = C_(0) + C_(1) x + C_(2)x^(2) + ...+ C_(n) x^(n) the cefficient of x^(n) in the expansion of (x + C_(0))(x + C_(1)) (x + C_(2))...(x + C_(n)) is

1 + (x)/( a_1) + ( x( x+a_1) )/( a_1 a_2 ) + .... + ( x ( x+a_1) (x+ a_2)... ( x+a_(n-1) ) )/( a_1 a_2 ..... a_n)=

Let a_1,a_2,a_3,.... are in GP. If a_n>a_m when n>m and a_1+a_n=66 while a_2*a_(n-1)=128 and sum_(i=1)^n a_i=126 , find the value of n .

S=sum_(i=1)^(n)sum_(j=1)^(i)sum_(k=1)^(j)1

If sum_(i=1)^n (x_i -a) =n and sum_(i=1)^n (x_i - a)^2 =na then the standard deviation of variate x_i