Repeating Patterns In Decimals Gmat, Gre Problem

What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?

A. 0
B. 1
C. 5
D. 7
E. 8





1/3=0.333
1/9=0.333/3=0.111
1/27=0.037 and repeats 
1/37=0.027 and repeats
Sum the first 3 digits in search of a pattern
0.111+0.333+0.027+0.037=0.508

After the 0 is a 5, then a 0, third digit is an 8 and the 4th is 5, 5th is a 0, 6th is an 8. 
Every 10th position we have a "change" 10th=5 20th=0 30th=8. That's the pattern.
100th=5 and then 101st=0

A