1/2+(1/3+2/3)+(1/4+2/4+3/4)+···+(1/10+2/10+···9/10) And this (1 + 1 / 2) * (1 + 1 / 4) * (1 + 1 / 6) * · * (1 + 1 / 10) * (1-1 / 3) * (1-1 / 5) * · * (1-1 / 9)

1/2+(1/3+2/3)+(1/4+2/4+3/4)+···+(1/10+2/10+···9/10) And this (1 + 1 / 2) * (1 + 1 / 4) * (1 + 1 / 6) * · * (1 + 1 / 10) * (1-1 / 3) * (1-1 / 5) * · * (1-1 / 9)

Calculate each item: 1 / K + 2 / K +.. + (k-1) / k = 1 / k * [1 + 2 +.. + (k-1)] = 1 / k * k (k-1) / 2 = (k-1) / 2, so 1 / 2 + (1 / 3 + 2 / 3) + (1 / 4 + 2 / 4 + 3 / 4) + ·· + (1 / 10 + 2 / 10 + ·· 9 / 10) = 1 / 2 + 2 / 2 + 3 / 2 +.. + 9 / 2 = 1 / 2 * (1 + 2 +.. + 9) = 1 / 2 * 9 * 10 / 2 = 45 / 2 (1 + 1 / 2) * (1 + 1