fractional sequence (denominator in arithmetic progression)

[Guest]

What is the formula to to solve the sum sequence:

1/1.1 + 1/1.2 + 1/1.3 + ... + 1/1.10

[HallsofIvy]

I don't understand your notation. Is [tex]1.3[/tex] a decimal? If so then 1.10 in the last fraction is the same as the 1.1 in the first. If it indicates a multiplication (better would be to use parentheses, not the ".") then multiplying by 1 doesn't change anything. This is just 1+ 1/2+ 1/3+ 1/4+ 1/5+ 1/6+ 1/7+ 1/8+ 1/9+ 1/10. And the only way to do that is to change to the "least common denominator (which is (8)(9)(5)(7)= 2520).