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Show that + 1/4 + (1.3)/(4.8) + (1.3.5)...

Show that ` + 1/4 + (1.3)/(4.8) + (1.3.5)/(4.8.12) + …….= sqrt2 `

Text Solution

Verified by Experts

The correct Answer is:
`sqrt2`
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Similar Questions

Explore conceptually related problems

1+(1)/(4) + (1.3)/(4.8) + (1.3.5)/(4.8.12)+…...=

1-(1)/(4)+(1.3)/(4.8)-(1.3.5)/(4.8.12)+…..=

Knowledge Check

  • 1 + 1/4 + (1.3)/(4.8) + (1.3.5)/(4.8.12) + ….." to " oo=

    A
    `sqrt2`
    B
    `(1)/(sqrt2)`
    C
    `sqrt3`
    D
    `(1)/(sqrt3)`

  • 1 + (1)/(4) + (1.3)/(4.8) + (1.3.5)/(4.8.12) + … is equal to

    A
    `sqrt2`
    B
    `(1)/(sqrt2) `
    C
    `sqrt3 `
    D
    `(1)/(sqrt3)`

  • Match the following. {:("I." 1+(1)/(3) + (1.3)/(3.6) + (1.3.5)/(3.6.9) +…....=, "a)" sqrt2),("II." 1+ (1)/(4) + (1.3)/(4.8) + (1.3. 5) /(4.8.12)=, "b)" 2 sqrt2),( "III." 1+(2)/(6) + (2.5)/(6.12) + (2.5.8)/(6.12.18)+…...=, "c)" sqrt3),( "IV." 1+(3)/(4) + (3.5)/(4.8) + (3.5.7)/(4.8.12)+........=, "d)" root(3)(4)):}

    A
    a, b, c, d
    B
    d, c, b, a
    C
    a, c, d, b
    D
    c, a, d, c

    • Similar Questions

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    Show that 1 - 3/4 + (3.5)/(4.8)- (3.5.7)/(4.8.12)+……..sqrt((8/27))

    1 + 2/4 + (2.5)/(4.8) + (2.5.8)/(4.8.12) + ….. =

    1+(1)/(4)+(1.4)/(4.8)+(1.4.7)/(4.8.12)+….=

    Show that (3)/(4.8)-(3.5)/(4.8.12) + (3.5.7)/(4.8.12.16) - …… = sqrt(2/3) -3/4

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