Let's calculate the sum of the numbers you provided:

$13 + 8 + 51 + 3 + 4 + 5 + 5 + 7 + 6 + 13 + 3 + 3 + 3 + 11 + 6 + 5 + 7 + 7 + 41 + 10 + 7 + 9 + 6 + 7 + 9 + 18 + 6 + 12 + 11 + 10 + 11 + 9 + 19 + 26 + 9 + 17 + 14 + 3 + 4 + 17 + 10 + 3 + 18 + 14 + 26 + 7 + 4 + 11 + 3 + 4 + 4$

To simplify the process, I'll add these step-by-step:

1. $13 + 8 = 21$
2. $21 + 51 = 72$
3. $72 + 3 = 75$
4. $75 + 4 = 79$
5. $79 + 5 = 84$
6. $84 + 5 = 89$
7. $89 + 7 = 96$
8. $96 + 6 = 102$
9. $102 + 13 = 115$
10. $115 + 3 = 118$
11. $118 + 3 = 121$
12. $121 + 3 = 124$
13. $124 + 11 = 135$
14. $135 + 6 = 141$
15. $141 + 5 = 146$
16. $146 + 7 = 153$
17. $153 + 7 = 160$
18. $160 + 41 = 201$
19. $201 + 10 = 211$
20. $211 + 7 = 218$
21. $218 + 9 = 227$
22. $227 + 6 = 233$
23. $233 + 7 = 240$
24. $240 + 9 = 249$
25. $249 + 18 = 267$
26. $267 + 6 = 273$
27. $273 + 12 = 285$
28. $285 + 11 = 296$
29. $296 + 10 = 306$
30. $306 + 11 = 317$
31. $317 + 9 = 326$
32. $326 + 19 = 345$
33. $345 + 26 = 371$
34. $371 + 9 = 380$
35. $380 + 17 = 397$
36. $397 + 14 = 411$
37. $411 + 3 = 414$
38. $414 + 4 = 418$
39. $418 + 17 = 435$
40. $435 + 10 = 445$
41. $445 + 3 = 448$
42. $448 + 18 = 466$
43. $466 + 14 = 480$
44. $480 + 26 = 506$
45. $506 + 7 = 513$
46. $513 + 4 = 517$
47. $517 + 11 = 528$
48. $528 + 3 = 531$
49. $531 + 4 = 535$
50. $535 + 4 = 539$

Thus, the total sum is 539.

Would you like more details on this, or is there any other part you'd like me to clarify?

Here are 5 related questions you might find interesting:

1. How do I check if my sum is correct using a calculator or different methods?
2. What are some strategies to add large lists of numbers efficiently?
3. How would I calculate the average of these numbers?
4. What is the mathematical significance of adding such large sets of numbers?
5. Can I calculate the sum of this list faster using software like Excel?

Tip: If you're ever adding large lists of numbers, grouping them in pairs or using the distributive property (breaking numbers down) can simplify your mental calculations!