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There is 1 seven followed by $2016 : 8 = 252$ groups of the numbers 1–8. The sum of the digits in each group is $\frac {8 \cdot 9}2 = 36$ , so the total sum is $7+252\cdot 36 \equiv 7 \mod 9$

This process of iteratedly calculating the digit sum gives the remainder when the number is divided by 9, which is 7 , as we just saw.

Put away the extension '7' from that sequence and there will be 2016 digits left with only 1-8 digits each of them 252 times.so the sum of that digit would be 252*(1+2+3+4+5+6+7+8)+7=9079. Now just add those digits again and again till you have one digit left.