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 t_1,t_2 and t_3 are distinct, the points (t_1, 2at_1 + at_1^3), (t_2, 2at_2 + at_2^3), (t_3, 2at_3 +at_3^3) are collinear then show that t_1+t_2+t_3=0 .

If t_1, t_2 and t_3 are distinct, the points (t_1, 2at_1+at_1^3), (t_2,2at_2+at_2^3) and (t_3,2at_3+at_3^3) are collinear if

Let S_n=sum_(k=0)^n n/(n^2+kn+k^2) and T_n=sum_(k=0)^(n-1) n/(n^2+kn+k^2) for n=1,2,3... then(correct options may be more than one) (a) S_n lt pi/(3sqrt(3)) b) S_n gt pi/(3sqrt(3)) (c) T_n lt pi/(3sqrt(3)) (d) T_n gt pi/(3sqrt(3))

Prove that by using the principle of mathematical induction for all n in N : (1)/(1.2.3)+ (1)/(2.3.4)+ (1)/(3.4.5)+....+ (1)/(n(n+1)(n+2))= (n(n+3))/(4(n+1)(n+2))

If the time taken by a particle moving at constant acceleration to travel equal distances along a straight line are t_(1), t_(2), t_(3) respectively prove that (1)/(t_(1))-(1)/(t_(2))+(1)/(t_(3))=(3)/(t_(1)+t_(2)+t_(3)) .

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/(t2 2))dot

If sum_(r=1)^nT_r =n/8(n+1)(n+2)(n+3) then find sum_(r=1)^n1/T_r

If the normals at P(t_(1))andQ(t_(2)) on the parabola meet on the same parabola, then (A) t_(1)t_(2)=-1 (B) t_(2)=-t_(1)-(2)/(t_(1)) (C) t_(1)t_(2)=1 (D) t_(1)t_(2)=2

If t_n denotes the nth term of the series 2+3+6+11+18+... then t_(50) a. 49^2-1 b. 49^2 c. 50^2+1 d. 49^2+2

Answer the following questions : (Alternatives are to be noted): If T_1 , T_2 , T_3 be estimators with expectations E(T_1) = theta_1+ 2theta_2 , E(T_2) = theta_2+2theta_3 , and E(T_3) = theta_3 + 2theta_1 find unbaised estimator of theta_1+theta_2+theta_3 .