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))=`

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 (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)

Suppose a series of n terms given by S_(n)=t_(1)+t_(2)+t_(3)+ . . . . +t_(n) then S_(n-1)=t_(1)+t_(2)+t_(3)+ . . . . +t_(n-1),nge1 subtracting we get S_(n)-S_(n-1)=t_(n),nge2 surther if we put n=1 is the first sum then S_(1)=t_(1) thus w can write t_(n)=S_(n)-S_(n-1),nge2 and t_(1)=S_(1) Q. The sum of n terms of a series is a.2^(n)-b . where a and b are constant then the series is

Suppose a series of n terms given by S_(n)=t_(1)+t_(2)+t_(3)+ . . .. +t_(n) then S_(n-1)=t_(1)+t_(2)+t_(3)+ . . . +t_(n-1),nge1 subtracting we get S_(n)-S_(n-1)=t_(n),nge2 surther if we put n=1 is the first sum then S_(1)=t_(1) thus w can write t_(n)=S_(n)-S_(n-1),nge2 and t_(1)=S_(1) Q. if the sum of n terms of a series a.2^(n)-b then the sum sum_(r=1)^(infty)(1)/(t_(r)) is

Let the n^(th) term of a series be given by t_n = (n^2 -n-2)/(n^2+3n),n leq 3 . Then product t_3 t_4 .....t_50 is equal to

Let the n^(th) term of a series be given by t_n = (n^2 -n-2)/(n^2+3n),n leq 3 . Then product t_3 t_4 .....t_50 is equal to

Let n_(th) term of the sequence be given by t_n = ((n+2)(n+3))/4 Assertion: 1/t_1+1/t_2+………..+1/t_2009=2009/1509 , Reason: 1/((n+2)(n+3))= 1/(n+2)-1/(n+3) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Which among the following relations is correct? (a) t_(3//4) = 2t_(1//2) (b) t_(3//4) = 3t_(1//2) (c) t_(3//4) = 1/2t_(1//2) (d) t_(3//4) = 1/3t_(1//2)

If a circle and the rectangular hyperbola xy = c^(2) meet in four points 't'_(1) , 't'_(2) , 't'_(3) " and " 't'_(4) then prove that t_(1) t_(2) t_(3) t_(4) = 1 .

If sum _(r =1) ^(n ) T _(r) = (n +1) ( n +2) ( n +3) then find sum _( r =1) ^(n) (1)/(T _(r))

If sum_(r=1)^n t_r= (n(n+1)(n+2))/3 then sum _(r=1)^oo 1/t_r= (A) -1 (B) 1 (C) 0 (D) none of these