The sum ` 1 + 3 + 3^(2) + …+ 3^(n)` is equal to

The sum of the series sum _( n =8) ^( 17) (1)/((n +2) (n +3)) is equal to

If 1+x^(2)=sqrt(3)x, then sum_(n=1)^(24)(x^(n)-(1)/(x^(n))) is equal to

The value of the sum_(n=0)^(oo)(2n+3)/(3^(n)) is equal to

The value of the sum 1.2.3+2.3.4+3.4.5+… upto n terms is equal to

The sum of the series sum_(n =8)^(17)1/((n + 2)(n + 3)) is equal to

Let n in N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms ""^(n) C_(0) , 3 .""^(n)C_(1) , 5. :""^(n) C_(2) , & .""^(n)C_(3) is equal to 2 ^(100) . 101 then 2 [(n-1)/(2)] is equal to _________