Problem 40

Champernowne's constant

An irrational decimal fraction is created by concatenating the positive integers:

0.123456789101112131415161718192021...

It can be seen that the 12^{th} digit of the fractional part is 1.

If *d*_{n} represents the *n*^{th} digit of the fractional part, find the value of the following expression.

*d*_{1}*d*_{10}*d*_{100}*d*_{1000}*d*_{10000}*d*_{100000}*d*_{1000000}

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