`(1.2)/(1!)+(2.3)/(2!)+(3.4)/(3!)+....=`

(1^(2).2)/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+....=

If 1^(2)+(2^(2))/(2!)+(3^(2))/(3!)+(4^(2))/(4!)+....=ae,(1^(2).2)/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+...=be,(1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+...=ce then the descending order of a,b,c is

The sum of the series ((1)^(2).2)/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+(4^(2).5)/(4!) +..is

The sum of the series ((1)^(2).2)/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+(4^(2).5)/(4!) +..is

If S_(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))/(n!) then lim_(n rarr infty) S_(n) is equal to