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

A

e

B

2e

C

`sqrte`

D

`e/2`

Verified by Experts

The correct Answer is:

B

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Explore conceptually related problems

(1.3)/(1!) +(2.4)/(2!)+(3.5)/(3!) + (4.6)/(4!) + .......oo = .......

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

(1/(1!) +1/(2!) +1/(3!) + .....oo) (1/(2!) -1/(3!) +1/(4!)-1/(5!) .....oo)

Cofficient of x^4 in 1+(1+x+x^2)/(1!) +((1+x+x^2)^2)/(2!) +((1+x+x^2)^3)/(3!) + ....oo =

1+ (1)/(10^2) + (1.3)/(1.2). (1)/(10^4) + (1.3.5)/(1.2.3) . (1)/(10^6) + …… oo =

If (1+1/(1!)+(1)/(2!)+......oo) (1-(1)/(1!) +1/(2!) -1/(3!) + ......oo)=

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

(1+3/(1!) +9/(2!) +(27)/(3!) + .....oo) (1+9/(1!) +(81)/(2!)+(729)/(3!)+ .....oo) =

1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+.....oo

If x = (1)/(1.2) + (1)/(3.4) + (1)/(5.6) …….oo, and y = 1 - (1)/(2.3) - (1)/(4.5) - (1)/(6.7)…….oo , then