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

There is a way to compute this Mathematics.

Those people that take up the subject in degree and major in Mathematics should know how to compute the figure in Logarithm up to the last 1000 digits manually.

Using the formula to compute Logarithm so as to achieve 1000th digit is possible.  After that, using the end result to find out the answer of this question.  However, it is very tedious.  I do not want to compute it.

The formula is quite complicated and I do not want to elaborate here.

Anybody wants to know the way how the number can be computed through the formula to obtain logarithm table should proceed to any libary for research and they will know the way to compute it.

Thanks.

Edited on April 29, 2005, 7:16 am

Posted by Jonathan Chang on 2005-04-29 07:03:10