What is the 1000th digit to the right of the decimal point in the decimal representation of (1+√2)^3000?

This problem can be solved by algebra alone, without the need for computers or calculators

(In reply to Solution by Federico Kereki)

Federico,

Nice solution, although I think you meant:

"10^(negative0.37x3000)< 10^(negative1000)"

I wasn't familiar with Newton's formula, so I had to work a few itterations to prove it to myself. Falls in the category of "learn something new every day".

Posted by Leming on 2005-04-27 00:42:33