`tan (A_1+A_2 +... + A_n) = (S_1-S_3+S_5-S_7+...) / (1 - S_2 + S_4 - S_6+...)`

If S_(1), S_(2), S_(3),….., S_(n) are the sum of infinite geometric series whose first terms are 1,3,5…., (2n-1) and whose common rations are 2/3, 2/5,…., (2)/(2n +1) respectively, then {(1)/(S_(1) S_(2)S_(3))+ (1)/(S_(2) S_(3) S_(4))+ (1)/(S_(3) S_(4)S_(5))+ ........."upon infinite terms"}=

Let S_(n)=1+2+3+...+n and P_(n)=(S_(2))/(S_(2)-1)*(S_(3))/(S_(3)-1)*(S_(4))/(S_(4)-1)...(S_(n))/(S_(n)-1) Where n in N,(n>=2). Then lim_(x rarr oo)P_(n)=

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 S_(1),S_(2),S_(3) be respectively the sum of n,2n and 3n terms of a GP, then (S_(1)(S_(3)-S_(2)))/((S_(2)-S_(1))^(2)) is equal to