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(1-(2)/(1!)+(4)/(2!)-(8)/(3!)+....)(1+(4...

`(1-(2)/(1!)+(4)/(2!)-(8)/(3!)+....)(1+(4)/(1!)+(16)/(2!)+(64)/(3!)+....)=`

A

e

B

`e^(2)`

C

`e^(3)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
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Explore conceptually related problems

If 1+(2)/(1!)+(4)/(2!)+(8)/(3!)+....=e^(a),1+(4)/(1!)+(16)/(2!)+(64)/(3!)+....=e^(b),1-(2)/(1!)+(4)/(2!)-(8)/(3!)+....=e^(c) then the ascending order of a, b, c is

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

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

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

(1+(2^(2))/(2!)+(2^(4))/(3!)+(2^(6))/(4!)+....)/(1+(1)/(2!)+(2)/(3!)+(2^(2))/(4!)+....)=

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