1+1/3+1/6+1/10+...+1/5050越快越好,

1+1/3+1/6+1/10+...+1/5050越快越好,
1+1/3+1/6+1/10+...+1/5050
越快越好,

1+1/3+1/6+1/10+...+1/5050越快越好,
裂项法
1+1/3+1/6+1/10+...+1/5050
=1+2/6+2/12+2/20+…+2/10100
=1+(2/2×3)+(2/3×4)+(2/4×5)+…+(2/100×101)
=1+2(1/2-1/3+1/3-1/4+1/4-1/5+…+1/100-1/101）
=1+2(1/2-1/101)
=200/101.