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

1. ## 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.

2. 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?