If `A_(i)= [(2^(-i),3^(-i)),(3^(-i),2^(-i))],then sum_(i=1)^(oo) det (A_(i))` is equal to

If A_(i)=[(a^(i),b^(i)),(b^(i),a^(i))] and |a| lt 1,|b| lt 1 then the value of sum_(i=1)^(oo) det (A_(i)) is -

If (a_(1)+ib_(1))(a_(2)+ib_(2))………………(a_(n)+ib_(n))=A+iB , then sum_(i=1)^(n) tan^(-1)(b_(i)/a_(i)) is equal to

If (a_(1)+ib_(1))(a_(2)+ib_(2))………………(a_(n)+ib_(n))=A+iB , then sum_(i=1)^(n) tan^(-1)(b_(i)/a_(i)) is equal to

If =1-a_(i),na=sum_(i=1)^(n)a_(i),nb=sum_(i=1)^(n)b_(i), then sum_(i=1)^(n)a_(i),b_(i)+sum_(i=1)^(n)(a_(i)-a)^(2)ab b.-nab c.(n+1)ab d.nab

if a,A_(1),A_(2),A_(3)......,A_(2n),b are in A.P.then sum_(i=1)^(2n)A_(i)=(a+b)

If a_(1),a_(2).........,a_(19) are the first 19 term of an AP and a_(1)+a_(8)+a_(12)+a_(19)=224 Then sum_(i=1)^(19)a_(i) is equal to :

If a_(1),a_(2),a_(3),... are in A.P.and a_(i)>0 for each i,then sum_(i=1)^(n)(n)/(a_(i+1)^((2)/(3))+a_(i+1)^((1)/(3))a_(i)^((1)/(3))+a_(i)^((2)/(3))) is equal to

Assertion: Given that prod_(i=1)^(n)a_(i)=1 where a_(1),a_(2),a_(3)a_(i)in R then minimum value of sum_(i=1)^(n)a_(i) integrs is greater than or equal to their geometric mean.