The pattern 123456790 is recurring. This is equivalent to the fraction 10/81. The series can be written as a sum=∑(r/10ʳ).
So the pattern contains 9 digits and the zero appears every 9th digit. The 108th digit is therefore zero. That makes the 114th digit 6.
Here is the reasoning:
10/81=10(1/9)²=10(1/(10-1))²=10[1/(10(1-0.1))²]=0.1(1-0.1)⁻².
The binomial expansion of this is 0.1(1+2/10+((-2)(-3)/2!)/100-((-2)(-3)(-4)/3!)/1000+...=
0.1(1.23456...).
This reduces to 0.1∑(r/10ʳ⁻¹)=∑(r/10ʳ) which is the given series.