∑[n!], n=7 to 2006 ≈2.145864201903033729347689996019583230087×10^5755
Counting from the left, the 10th digit is 1. But your question is: "What is the tens digit", which means the second last digit, which is a 4. Not sure which one you mean!.
All you need to add for your purpose are 4 numbers from the start and 4 numbers from the end:
7! + 8! + 9! + 10! +.................+ 2003! + 2004! + 2005! + 2006!=
214586420190..................40. All the other numbers in between are not going to change the 10th digit from the left, or "tens" digit from the right.
