Alternative Series II
1. 
, where
.
2. 
.
.3. 
.
.4. 
.
. or
.5. 
.
.6. 
.
.7. 
.
.8. 
.
.9. 
.
.10. 
.
.11. 
.
.12. 
.
.13. 
,
,where
.
. 
, etc.14. 
.
.15. 
.
.16. 
.
.17. 
.
.18. 
.
.19. 
.
.20. 
.
.21. 
.
.
, where 
is Euler Constant (see 23. 
.
.24. 
.
.25. 
.
.26. 
.
.27. 
.
.Recall that 
.
.28. 
.
.29. 
.
.30. 
.
.31. 
.
.32. 
.
.33. 
.
.34. 
.
.35. 
.
.36. 
.
.or 
.
.37. 
.
.38. 
.
.39. 
.
.40. 
.
.41. 
.
.42. 
.
.43. 
.
.44. 
.
.45. 
.
.46. 
.
.47. 
.
.48. 
.
.49. 
.
.50. 
, where n is an integer.
, where n is an integer.(The exact sum of the first n terms of harmonic series can be calculated)
51. 
, where 
.
, where .52. 
, where 
.
, where .53. 
.
.