If `t_n=1/4(n+2)(n+3)` for `n=1, 2 ,3,....` then `1/t_1+1/t_2+1/t_3+....+1/(t_(2003))=`

If the normals at points t_1a n dt_2 meet on the parabola, then t_1t_2=1 (b) t_2=-t_1-2/(t_1) t_1t_2=2 (d) none of these

If the sequence t_(1), t_(2), t_(3), … are in A.P. then the sequence t_(6), t_(12), t_(18),… is

If t_(n)" is the " n^(th) term of an A.P. then the value of t_(n+1) -t_(n-1) is ……

The base of a triangle is divided into three equal parts. If t_1, t_2,t_3 are the tangents of the angles subtended by these parts at the opposite vertex, prove that (1/(t_1)+1/(t_2))(1/(t_2)+1/(t_3))=4(1+1/t_2^2)dot

Statement 1 : If a circle S=0 intersects a hyperbola x y=4 at four points, three of them being (2, 2), (4, 1) and (6,2/3), then the coordinates of the fourth point are (1/4,16) . Statement 2 : If a circle S=0 intersects a hyperbola x y=c^2 at t_1,t_2,t_3, and t_4 then t_1.t_2.t_3.t_4=1

If n >1,t h e np rov et h a t 1/((log)_2n)+1/((log)_3n)++1/((log)_(53)n)=1/((log)_(53 !)n)dot

If Sigma_(r=1)^(n) T_r=n/8(n+1)(n+2)(n+3) then find Sigma_(r=1)^(n) 1/T_r

Let C be incircle of A B Cdot If the tangents of lengths t_1,t_2a n dt_3 are drawn inside the given triangle parallel to sidese a , ba n dc , respectively, the (t_1)/a+(t_2)/b+(t_3)/c is equal to 0 (b) 1 (c) 2 (d) 3