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_n=sum_1^n n , find S_n=sum_1^n t_n .

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 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.

If ∑_ (i = 1)^T T y = ( n^ 2 + 3 n )^ 2 + 2 ⋅ ( n^ 2 + 3 n ) , then ∑_ (k =1)^oo 1/ (Tn) is

If t_(n)=(1+(-2)^(n))/(n-1) , find t_(6)-t_(5)

In a series, if t_n = (n^(2) -1)/(n+1) , then S_6 - S_3= _______.

If t_(n) = 1/((n+1)!) , then sum_(n=1)^(infty) t_(n)=