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
Please read the question carefully before you tackle it. The question is not interested on 1st or 2nd or 3th..or....999th digit. So, even if you provide me with the answer for 1st to 8th digits, the answer is wrong. The question demands you to have 1000th digit only. Just one number and not more than one. The answer must be accurate up to 1000th digit. Even the calculator that computes the square root of 2 can only give you a few digits of accuracy,ie. 1.412.. How about the rest of the digits continue behind. As the computation needs 1000th digit of accuracy, you must compute the square root of 2 up to at least 1000th digit so as to achieve the accuracy of this question.
The question is not interested in any formula that is furnished by you'll.
Use your calculator to compute the answer from the question. Your answer for the first 8 digits must be almost the same as the calculator then you can be qualified for championship for this game.
So, anyone of you are interested to solve this puzzle should show me that 3 is not the correct answer at 1000th digit. If not, sorry to say, 3 is the 1000th digit.
Come on! Try to solve this puzzle to be the champion of Perplexus.info.
Thanks.
Edited on April 28, 2005, 1:06 am
Solution
