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How to add fractions?

i dont know how to add 1/100+1/101+1/102+...+1/200

Does it have a formula?

2 Answers

  • 10 years ago
    Favorite Answer

    That's called a Harmonic Series, and you can look it up in Wikipedia.

    There's no simple formula for the sum of a harmonic series, but an approximation for the sum of the first n terms of the series 1/k is ln(k+1). So you could go ln(201) - ln(100) to get pretty close to the answer.

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  • 10 years ago

    Use this formula :

    Sn = n [2a+ (n-1)b ] / 2


    Sn : The sum of arithmatic series

    a = The 1st value of the series

    b = the difference between two close series

    and we get,

    n = 201

    a = 1/100

    b = 1/101 - 1/100 = 0,1/1010

    substitute the value above to the formula,

    So, we get the Sn = 4,0009

    Source(s): My lesson in Senior High School
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