If `sum_(i=1)^(10)tan^(-1)((3)/(9r^(2)+3r-1))=cot^(-1)((m)/(n))` (where m and n are coprime) then the value of `(2m+n)/(8)` is

If theta=tan^(-1)((1)/(10))+tan^(-1)((1)/(9))+...+tan^(-1)(1)+tan^(-1)(2)+...+tan^(-1)(10)+tan^(-1)(11) .If tan theta=(m)/(n) (where m,n are coprime) then the value of (m+n) is equal to

Let S_(n) and Delta_(n) be the sum of first n terms of 2A.P' 's whose r_(th) term are T_(r) and t_(r) respectively.If (S_(n))/(Delta_(n))=(2n+5)/(3n+2) then (T_(11))/(t_(10))=(m_(1))/(m_(2)) where m_(1) and m_(2) are coprime. Find the value of (m_(2)-m_(1))/(2) = ?

Let S_(n) and Delta_(n) be the sum of first n terms of 2 A. P' s whose rth term are T_(r) and t_(r) respectively.If (S_(n))/(Delta_(n))=(2n+5)/(3n+2) then (T_(11))/(t_(11))=(m_(1))/(m_(2)) where m_(1) and m_(2) are coprime. Find the value of (m_(2)-m_(1))/(2)=

(tan^(-1)((1)/(3))+tan^(-1)((1)/(7))+tan^(-1)((1)/(13))+......+tan^(-1)((1)/(381)))=(m)/(n) where m,n in N, then find least value of (m+n)

m sum_(r=1)^(n)(1)/(n)sqrt((n+r)/(n-r))

If sum_(r=1)^(n)r^(3)((C(n,r))/(C(n,r-1)))=14^(2) then n=

If sum_(r=1)^(n) r(sqrt(10))/(3)sum_(r=1)^(n)r^(2),sum_(r=1)^(n) r^(3) are in G.P., then the value of n, is