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Math Help - I found the answer using a calculator, but how can this be done analytically?

  1. #1
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    I found the answer using a calculator, but how can this be done analytically?

    Write down the numbers 2, 3, . . . , 100, together with
    their products taken two at a time, the products taken three at a time, and
    so on up to and including the product of all 99 of them. Find the sum of
    the reciprocals of the numbers written down.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Consider the product

    \left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\righ  t)\dots\left(1+\frac{1}{100}\right).

    If you expand it, you get what you are looking for, plus 1 because of the term 1 \times 1 \times \dots \times 1.

    Now can you find an expression for this product?
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