Let `T_(k)=(3)/((k+2)(k+3))`. Then `(T_(1)+T_(2)+T_(3)+......`infinite terms) = ?

Let the n^(th) term of a series be given by t_(n)=(n^(2)-n-2)/(n^(2)+3n),n<=3. Then product t_(3)t_(4).....t_(50) is equal to

A mass is suspended separately by two springs and the time periods in the two cases are T_(1) and T_(2) . Now the same mass is connected in parallel (K = K_(1) + K_(2)) with the springs and the time is suppose T_(P) . Similarly time period in series is T_(S) , then find the relation between T_(1),T_(2) and T_(P) in the first case and T_(1),T_(2) and T_(S) in the second case.

Let T_(k)=sin^(k)x+cos^(k)x For all x if T_(1)T_(5)+T_(3)T_(5)=T_(1)T_(7)+T_(3)T_(n) then n=

If K_(1) and K_(2) are equilibrium constants at T_(1) and T_(2) temperatures ( T_(1) > T_(2) ) ,then which of the following are correct? (A) When Delta H=+ve, K_(2) > K_(1) (B) When Delta H=0 K_(1) = K_(2) (C) When Delta H=-ve K_(2) (D) When Delta H=+ve K_(2) < K_(1)

Let vec(V) =v_(x)hat(i)+v_(y)hat(j)+v_(z)hat(k) , then int_(t_(1))^(t_(2)) V_(y) represents: (for the duration t_(1) to t_(2))

The Fibonacci sequence is defence by t_(1)=t_(2)=1,t_(n)=t_(n-1)+t_(n-2)(n>2). If t_(n+1)=kt_(n) then find the values of k for n=1,2,3 and 4.