If for a sequence `(T_(n)), (i) S_(n) = 2n^(2)+3n+1 (ii) S_(n) =2 (3^(n)-1) ` find `T_(n)` and hence `T_(1)` and `T_(2)`

If for n sequences S_(n)=2(3^(n)-1) , then the third term is

The sum S_(n) where T_(n) = (-1)^(n) (n^(2) + n +1)/( n!) is

Show that the sequence t_(n) defined by t_(n)=2*3^(n)+1 is not a GP.

Show that the the sequence defined by T_(n) = 3n^(2) +2 is not an AP.

The absolute value of the sum of first 20 terms of series, if S_(n)=(n+1)/(2) and (T_(n-1))/(T_(n))=(1)/(n^(2))-1 , where n is odd, given S_(n) and T_(n) denotes sum of first n terms and n^(th) terms of the series

The first two terms of a sequence are 0 and 1, The n ^(th) terms T _(n) = 2 T _(n-1) - T _(n-2) , n ge 3. For example the third terms T _(3) = 2 T_(2) - T_(1) = 2 -0=2, The sum of the first 2006 terms of this sequence is :

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

Tangents and normal from a point (3, 1) to circle C whose equation x^(2) + y^(2) - 2x - 2y + 1 = 0 Let the points of contact of tangents be T_(i)(x_(i),(y_(i)), where I = 1, 2 and feet of normal be N_(1) and N_(2)( N_(1) " is near" P) Tangents ared drawn at N_(1) and N_(2) and normals are drawn at T_(1) and T_(2)

If (1 ^(2) - t _(1)) + (2 ^(2) - t _(2)) + ......+ ( n ^(2) - t _(n)) =(1)/(3) n ( n ^(2) -1 ), then t _(n) is

If T_(n)=cos^(n)theta+sin ^(n)theta, then 2T_(6)-3T_(4)+1=