The sum `sum_(n=1)^oo (n/(n^4+4))` is equal to `p/q` then q-p is ____

sum_(n=1)^(oo)(n^(2))/(n!) is equal to

sum_(n=1)^(oo) ((Inx)^(n))/(n!) is equal to

The sum sum_(n=1)^(oo)tan^(-1)((3)/(n^(2)+n-1)) is equal to

sum_(n=0)^(oo)((log_(e)x)^(n))/(n!) is equal to

The value of sum_(n=1)^(oo)(1)/((3n-2)(3n+1)) is equal to (p)/(q), where p and q are relatively prime natural numbers.Then the value of (p^(2)+q^(2)) is equal to

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

sum_(n=1)^(oo)tan^(-1)((8)/(4n^(2)-4n+1)) is equal to

The value of sum_(n=3)^(oo)(1)/(n^(5) - 5n^(3) +4 n) is equal to -

Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :

Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :