0
|
3815 Views
|
3 Replies
|
3 Total Likes
View groups...
Share
GROUPS:

# Calculating infinite sum of a series

Posted 9 years ago
 I was curious about whether or not it was possible to make a fraction whose decimal expansion is all integers consecutively, i.e., 0.123456789101112... to infinity. I ended up expressing this value as the infinite sum of a sequence: Sum[(10^((1/9) (-9 10^n n + 10^n - 10)) ((10^n)^(9 10^(n - 1)) (-10^n + 100^n + 10) - 10 (-10^n + 100^n + 1)))/(10^n - 1)^2, {n, 1, Infinity}]  This sequence generates a decimal expansion which goes up to the integer 10^x-1.where x is the upper bound of the summation. When I enter this into wolfram it doesn't provide any insight other than that the sum converges. I was just wondering if there was a way to simplify this further into a function in terms of x and whether this value can be expressed as a fraction at all. Is it irrational? Any insight at all would be very helpful.
3 Replies
Sort By:
Posted 9 years ago
 And of course there is a Wolfram Language Function for that: N[ChampernowneNumber[10], 25] (*0.1234567891011121314151617*) Cheers,M.
Posted 9 years ago
 PerhapsChampernowne Constantor thisChampernowne Constantmight provide a little information for you.
Posted 9 years ago
 Thank you! You're my hero.