Let `s_1,s_2,s_3, .. and t_1,t_2,t_3....`. are two arithmetic sequences such that `s_1=t_1!=0,s_2=2t_2` and `sum_(i=1)^(10)s_1=sum_(i=1)^15 t_1` .Then the value of `(s_2-s_1)/(t_2-t_1)` is

Let s_(1), s_(2), s_(3).... and t_(1), t_(2), t_(3) .... are two arithmetic sequences such that s_(1) = t_(1) != 0, s_(2) = 2t_(2) and sum_(i=1)^(10) s_(i) = sum_(i=1)^(15) t_(i) . Then the value of (s_(2) -s_(1))/(t_(2) - t_(1)) is

Let s_(1), s_(2), s_(3).... and t_(1), t_(2), t_(3) .... are two arithmetic sequences such that s_(1) = t_(1) != 0, s_(2) = 2t_(2) and sum_(i=1)^(10) s_(i) = sum_(i=1)^(15) t_(i) . Then the value of (s_(2) -s_(1))/(t_(2) - t_(1)) is

If s=(t^(3))/(3)-(1)/(2)t^(2)-6t+5 , Find the value of (d^(2)s)/(dt^(2)) at t=1

If s=(t^(3))/(3)-(1)/(2)t^(2)-6t+5 , Find the value of (d^(2)s)/(dt^(2)) at t=1

If 3s+5t=10 , and 2s-t=7 , what is the value of (1)/(2^(s))+3t ?

Let a_(1), a_(2),....a_(3) be an AP, S = sum_(i = 1)^(30) a_(i) and T = sum_(i=1)^(15) a_((2i-1)) . If a_(5) = 27 and S -2T = 75 , then a_(10) is equal to

If sum of n termsof a sequende is S_n then its nth term t_n=S_n-S_(n-1) . This relation is vale for all ngt-1 provided S_0= 0. But if S_!=0 , then the relation is valid ony for nge2 and in hat cast t_1 can be obtained by the relation t_1=S_1. Also if nth term of a sequence t_1=S_n-S_(n-1) then sum of n term of the sequence can be obtained by putting n=1,2,3,.n and adding them. Thus sum_(n=1)^n t_n=S_n-S_0. if S_0=0, then sum_(n=1)^n t_n=S_n. On the basis of above information answer thefollowing questions:If nth term of a sequence is n/(1+n^2+n^4) then the sum of its first n terms is (A) (n^2+n)/(1+n+n^2) (B) (n^2-n)/(1+n+n^2) (C) (n^2+n)/(1-n+n^2) (D) (n^2+n)/(2(1+n+n^2)

If sum of n termsof a sequende is S_n then its nth term t_n=S_n-S_(n-1) . This relation is vale for all ngt-1 provided S_0= 0. But if S_!=0 , then the relation is valid ony for nge2 and in hat cast t_1 can be obtained by the relation t_1=S_1. Also if nth term of a sequence t_1=S_n-S_(n-1) then sum of n term of the sequence can be obtained by putting n=1,2,3,.n and adding them. Thus sum_(n=1)^n t_n=S_n-S_0. if S_0=0, then sum_(n=1)^n t_n=S_n. On the basis of above information answer thefollowing questions:If nth term of a sequence is n/(1+n^2+n^4) then the sum of its first n terms is (A) (n^2+n)/(1+n+n^2) (B) (n^2-n)/(1+n+n^2) (C) (n^2+n)/(1-n+n^2) (D) (n^2+n)/(2(1+n+n^2)

If area of pentagon PQRST be 7 ,where P(-1,-1),Q(2,0),R(3,1),S(2,2) and T(-1,t),t>0, then the value of t is

if P(t^(2),-2t) and Q((1)/(t^(2)),-(2)/(t)) and S(1,0) be any three points,find the value of ((1)/(SP)+(1)/(SQ))