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Math Help - Infinite Series

  1. #1
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    Infinite Series

    Show : (\frac{1}{1*3})+ (\frac{1}{2*4})+ (\frac{1}{3*5})+.....=\frac{3}{4}

    When i do the problem i keep getting \frac{3}{2}instead of [tex]\frac{3}{4}/MATH]
    Heres how im doing it
    (1-\frac{1}{3})+(\frac{1}{2}-\frac{1}{4})+(\frac{1}{3}-\frac{1}{5})+...
    which gives me as the lim n appraoches infinity (\frac{3}{2}-\frac{1}{n+2})
    I dont see where i am going wrong or how to get \frac{3}{4}
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  2. #2
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    Hello, vinson24!

    You missed a fraction in your Partial Fractions . . .


    Show that: . \frac{1}{1\cdot3}+ \frac{1}{2\cdot4}+ \frac{1}{3\cdot5}+ \hdots \;=\;\frac{3}{4}

    When i do the problem i keep getting \frac{3}{2} instead of \frac{3}{4}

    Here's how I'm doing it:

    \left(1-\frac{1}{3}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+ \hdots . Here!


    . . \frac{1}{n\cdot(n+2)}\;=\;{\color{red}\frac{1}{2}}  \,\bigg[\frac{1}{n} - \frac{1}{n+2}\bigg]

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  3. #3
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    With the way you do it I'm getting 1/2
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