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

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

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(e^(2)+1)/(e^(2)-1) =(1 + (1)/(2!) + (1)/(4!) + (!)/(6!) +...)/(1 +(1)/(3!) + (!)/(5!) + (1)/(7!) +...)

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Knowledge Check

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

    A
    `e+1`
    B
    `(e-1)/(e+1)`
    C
    `e-1`
    D
    0
  • Show that (1 + (1)/(2!) + (2)/(3!) + (2^(2))/(4!) + (2^(3))/(5!) +...)/(1+(1)/(2!) +(1)/(4!)+(1)/(6!) +...) =

    A
    `(e)/(2)`
    B
    `e^(2)-1`
    C
    `(e+1)/(e-1)`
    D
    4e
  • The value of 3 (1)/(2) - [2 (1)/(4) + {1 (1)/(4) - (1)/(2)(1 (1)/(2) - (1)/(3) - (1)/(6))}] is

    A
    `(1)/(2)`
    B
    `2 (1)/(2)`
    C
    `3 (1)/(2)`
    D
    `9 (1)/(2)`
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    The sum of the series 1 + ((1)/(2) + (1)/(3)) (1)/(4) + ((1)/(4) + (1)/(5)) (1)/(4^(2)) + ((1)/(6) + (1)/(7)) (1)/(4^(3)) + ...oo

    (9)/(20) - [(1)/(5) + {(1)/(4) + ((5)/(6) - bar((1)/(3) + (1)/(2)))}] is equal to

    5 (1)/(5) - [3 (1)/(2) - {(5)/(6) - ((3)/(5) + (1)/(10)-(4)/(15)}] is equal to :

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