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

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

A

`e-1`

B

`e^(2)-1`

C

`e+1`

D

`e^(2)+1`

Text Solution

Verified by Experts

The correct Answer is:
B
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1^(2)+(2^(2))/(2!)+(3^(2))/(3!)+(4^(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

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

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

DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1A
  1. (1+(1)/(2!)+(1)/(4!)+(1)/(6!)+....)^(2)-(1+(1)/(3!)+(1)/(5!)+(1)/(7!)+...

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  2. (1+(a^(2)x^(2))/(2!)+(a^(4)x^(4))/(4!)+....)^(2)-(ax+(a^(3)x^(3))/(3!)...

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

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  4. (1+(1)/(3!)+(1)/(5!)+....)/(1+(1)/(2!)+(1)/(4!)+....)=

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  5. ((1)/(2!)+(1)/(4!)+(1)/(6!)+....)/(1+(1)/(3!)+(1)/(5!)+....)=

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  6. (1)/(2)-(1)/(3(1!))+(1)/(4(2!))-(1)/(5(3!))+....=

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  7. (1)/(1!)+(1+2)/(2!)+(1+2+2^(2))/(3!)+....=

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  8. (1)/(1!)+(1+3)/(2!)+(1+3+3^(2))/(3!)+....=

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  9. (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+....

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  10. (2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+....=

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  11. (1)/(1!)+(1+3)/(2!)+(1+3+3^(2))/(3!)+....=

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  12. 1^(2)+(2^(2))/(2!)+(3^(2))/(3!)+(4^(2))/(4!)+....=

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  13. (1^(2))/(2!)+(2^(2))/(3!)+(3^(2))/(4!)+....=

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  14. (1^(2))/(1!)+(1^(2)+2^(2))/(2!)+(1^(2)+2^(2)+3^(2))/(3!)+....=

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  15. (1^(2).2)/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+....=

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  16. (1^(2).2^(2))/(1!)+(2^(2).3^(2))/(2!)+(3^(2).4^(2))/(3!)+....=

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  17. underset(n=1)overset(oo)sum.^(n)C(0)+.^(n)C(1)+underset(.^(n)P(n))(.^(...

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  18. 1-(x^(2))/(2!)+(x^(4))/(4!)-(x^(6))/(6!)+....=

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  19. (1.2)/(1!)+(2.3)/(2!)+(3.4)/(3!)+....=

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  20. 1+(1)/(2!)+(1.3)/(4!)+(1.3.5)/(6!)+...=

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