If `S=1/(1+1^2+1^4)+2/(1+2^2+2^4)+3/(1+3^2+3^4)+.........oo,` then find the value of `14S.`

If S=(1)/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+...."to "oo , then S =

S_(n)=(1.2)/(3)+(2.3)/(3^(2))+(3.4)/(3^(3))......oo, then 4S is

1 + (1+2)/(2!) + (1+2+3)/(3!) + (1+2+3+4)/(4!) + ......oo

If {:(1,2,4),(1,3,5),(1,4,a):} is singular then the value of a is

Let S_1 = 4+6/3+8/3^2+10/3^3+...+oo and S_2 =sum_(n=1)^oo 1/((3n+1)(3n+4)), then the value of the S_1/(10 S_2) is