MATH / Consider this pattern where the positive, proper fractions with denominator…

Consider this pattern where the positive, proper fractions with denominator (n+1)  are arranged in the nth row in a triangular formation. The 1st through 4th rows are shown; each row has one more entry than the previous row. What is the sum of the fractions in the 15th row?

[asy]
label("(1)/(2)",(0,0),S);
label("(1)/(3)",(-5,-5),S);
label("(2)/(3)",(5,-5),S);
label("(1)/(4)",(-10,-10),S);
label("(2)/(4)",(0,-10),S);
label("(3)/(4)",(10,-10),S);
label("(1)/(5)",(-15,-15),S);
label("(2)/(5)",(-5,-15),S);
label("(3)/(5)",(5,-15),S);
label("(4)/(5)",(15,-15),S);
dot((0,-22));
dot((0,-20));
dot((0,-24));
[/asy]

Consider this pattern where the positive, proper fractions with denominator $(n+1)$  are arranged in the $n$th row in a triangular formation. The 1st through 4th rows are shown; each row has one more entry than the previous row. What is the sum of the fractions in the 15th row?

[asy]
label("$\frac{1}{2}$",(0,0),S);
label("$\frac{1}{3}$",(-5,-5),S);
label("$\frac{2}{3}$",(5,-5),S);
label("$\frac{1}{4}$",(-10,-10),S);
label("$\frac{2}{4}$",(0,-10),S);
label("$\frac{3}{4}$",(10,-10),S);
label("$\frac{1}{5}$",(-15,-15),S);
label("$\frac{2}{5}$",(-5,-15),S);
label("$\frac{3}{5}$",(5,-15),S);
label("$\frac{4}{5}$",(15,-15),S);
dot((0,-22));
dot((0,-20));
dot((0,-24));
[/asy]