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
The question mentions that we cannot use computer or calculator to compute.
The Logarithm book or the computer could only give the most up to the maximum of 8 digits, how to compute with such an accuracy up to 1000th digit. It is impossible.
Lg(0.42) = -0.37 (You can have the most 4 figures or five from Logarithm books. For computer, the most 8 digits accuracy. To have 1000th digit accuracy, it is impossible.)
Even if you use Logarithem book or the computer, you could not compute accurately since the question wants 1000th digit of it. A slight difference of 0.0001 could cause the 1000th figure to be different.
Could anybody prove that the answer of this question is 3 is wrong? If nobody could prove that it is wrong, let's take this to be the answer of the question.
Thanks.
Edited on April 27, 2005, 4:36 am
Edited on April 27, 2005, 4:39 am
Solution
