IIT JEE , AIEEE Forum - Mathematics , Algebra

nicKOOL09

(1)1²/2!+2²/2!+3²/4!+................

nadeemoidu

Is the answer 'e'?

and should n't it be 1²/2! + 2²/3! + 3²/4! +.

nicKOOL09

no the ans is e-1 please try......

nadeemoidu

General term,
$T_k= rac{k^2}{(k+1)!}$

$= rac{k^2-1+1}{(k+1)!}$

= rac{k-1}{(k)!} + rac{1}{(k+1)!}

Now ,
$\sum_{k=1}^\infty \frac{1}{(k-1)!} - \frac{1}{k!}+ \frac{1}{(k+1)!}$ = (e) - (e-1) +(e-2)

= e-1

nicKOOL09

thanks yaar i got it........