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2/1! + 4/3! + 6/5! + . . . . . . . .=e

2/1! + 4/3! + 6/5! + . . . . . . . .=e 

Grade:12th Pass

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago
nth term of the series Tn=2n/(2n-1)!
=(2n-1+1)/(2n-1)!
=1/(2n-2)!+1/(2n-1)!
putting n=1,2,3,...........
T1=1/0!+1/1!
T2=1/2!+1/3!
T3=1/4!+1/5!
..........................
.........................
Adding all these terms on both sides, we get
T1+T2+T3+..............=1+1/1!+1/2!+1/3!+............=e

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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