Find the first digit before and after the decimal point in the base ten expansion of (√2 + √3)^{2011}.
For an extra challenge, solve this puzzle without using a computer program.
(In reply to
The Broll guesses... by broll)
Why did you stop at (a+b)^2000?
Your reasoning breaks down if you instead use a different large even power:
= (a+b)^2002*(a+b)^9
=(something huge)+0.9999999999........9*(a+b)^9
(a+b)^9= 30210.4301525
so the digits before and after the decimal point should be ...0.4...?

Posted by Jer
on 20110325 14:28:25 