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
(In reply to
Solution by Jonathan Chang)
Seeing that 0.42^3000 is less than 10^1000 is enough to guarantee that the fraction part of (1+√2)^3000 is .9999...999 with at least
1000 nines. More precision could tell you exactly how many nines, and
even what's the first "not-nine" digit, but taht's not asked for.
re: Solution
