Find the value `n + ( 3n )/(2) + ( 9n)/(4) + ...oo.`

Let {a _(n)} _( n -1) ^(oo) be a sequene such that a _(1) = 1, a _(2) = 1 and a _( n+2) = 2 a _( n +1) + a _(n) for all n ge 1. Then the value of 47 sum _( n -1) ^(oo) ( a _(n))/( 2 ^( 3n)) is equal to ____________.

Find the value of (3^(n)xx3^(2n+1))/(9^(n)xx3^(n-1)) .

Find the value of (3^(12+n)xx9^(2n-7))/(3^(5n))

Find lim_ (n rarr oo) (4n ^ (2) + 6n + 2) / (4) n ^ (2)

Find the value of lim_(n rarr oo)(1)/(n)+(1)/(n+1)+(1)/(n+2)+...+(1)/(4n)

The value of sum_(n=1)^(oo)(4n-2)/(3^(n))

The value of lim_(n to oo) (2n^(2) - 3n + 1)/(5n^(2) + 4n + 2) equals

Find the value of lim_(n rarr oo)sum_(r=1)^(n)(r^(2))/(n^(3)+n^(2)+r)

Find the value of lim_(n to oo) (tan(sum_(r=1)^(n) tan^(-1)((4)/(4r^(2)+3)))) .