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1000th digit (Posted on 2005-04-26) Difficulty: 3 of 5
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

See The Solution Submitted by Pemmadu Raghu Ramaiah    
Rating: 3.3750 (8 votes)

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Some Thoughts Chang = Intentionally obtuse? | Comment 29 of 30 |
If I subtract a number LESS than 10^-1 from an integer, how does the fractional part of the result start? ANSWER: .9... -- the first digit is a 9.

If I subtract a number LESS than 10^-2 from an integer, how does the fractional part of the result start? ANSWER: .99... -- the second digit is a 9.

If I subtract a number LESS than 10^-3 from an integer, how does the fractional part of the result start? ANSWER: .999... -- the third digit is a 9.

Do you need 997 more lines to explain the solution to this problem?


Edited on April 29, 2005, 4:09 pm
  Posted by Old Original Oskar! on 2005-04-29 16:08:19

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