Sum of series.. from Hall and Knight

This might seem so very tough..

just remember:

1) e=1+1+1/2!+1/3!+1/4!...............

2) Also write the above expression as a summation and see if u can break it down into such a sum...

It is not very easy... but a little manipulation is needed!

try for 5-10 minutes.. and tell me.. i will solve this for u after that :)

S = Σ(1 to ∞) r³/r!

S = Σ(1 to ∞) r²/(r-1)!

S = Σ(1 to ∞) (r²-1+1)/(r-1)!

S = Σ(1 to ∞) ((r-1)(r+1)+1)/(r-1)!

S = Σ(1 to ∞) {(r-1)(r+1)/(r-1)! +1/(r-1)!

S = Σ(1 to ∞) {(r+1)/(r-2)! +1/(r-1)!}

S = Σ(1 to ∞) (r+1)/(r-2)! +Σ(1 to ∞) 1/(r-1)!

S = Σ(1 to ∞) (r+1)/(r-2)! + e

keep going this way ....just a very few steps that are left...