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Find the sum of the following series: 1...

Find the sum of the following series: `1/2+1/(3^2)+1/(2^3)+1/(3^4)+1/(2^5)+1/(3^6)+oo`

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Find the sum of the following infinite series (1)/(2)((1)/(5))^(2)+(2)/(3)((1)/(5))^(3)+(3)/(4)((1)/(5))^(4)+...

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Knowledge Check

  • The sum of the infinite series (1/3)^(2)+1/3(1/3)^(4)+1/5(1/3)^(6)+ . . . is

    A
    `1/4log_(e)2`
    B
    `1/2log_(e)2`
    C
    `1/6log_(e)2`
    D
    `1/4"log"_(e)3/2`

  • The sum of the infinite series (1)/(2) ((1)/(3) + (1)/(4)) - (1)/(4)((1)/(3^(2)) + (1)/(4^(2))) + (1)/(6) ((1)/(3^(3)) + (1)/(4^(3))) - ...is equal to

    A
    `(1)/(2) log 2`
    B
    `log (3)/(5)`
    C
    `log(5)/(3)`
    D
    `(1)/(2) log(5/3)`

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