求(1-1/2+1/3-1/4+……+1/99-1/100)/{1/(1+101)+1/(2+102)+……+1/(50150)的值
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![求(1-1/2+1/3-1/4+……+1/99-1/100)/{1/(1+101)+1/(2+102)+……+1/(50150)的值](/uploads/image/z/668133-45-3.jpg?t=%E6%B1%82%EF%BC%881-1%2F2%2B1%2F3-1%2F4%2B%E2%80%A6%E2%80%A6%2B1%2F99-1%2F100%EF%BC%89%2F%EF%BD%9B1%2F%EF%BC%881%2B101%EF%BC%89%2B1%2F%EF%BC%882%2B102%29%2B%E2%80%A6%E2%80%A6%2B1%2F%2850150%29%E7%9A%84%E5%80%BC)
求(1-1/2+1/3-1/4+……+1/99-1/100)/{1/(1+101)+1/(2+102)+……+1/(50150)的值
求(1-1/2+1/3-1/4+……+1/99-1/100)/{1/(1+101)+1/(2+102)+……+1/(50150)的值
求(1-1/2+1/3-1/4+……+1/99-1/100)/{1/(1+101)+1/(2+102)+……+1/(50150)的值
分子
=(1+1/2+1/3+1/4+……+1/99+1/100)-2*(1/2+1/4+……+1/100)
=1/51+……+1/99+1/100
分母
=1/2 * (1/51+……+1/99+1/100)
原
=1/2
令G=1+1/3+1/5+...+1/99;H=1/2+1/4+...+1/100;I=1/51+1/52+...+1/100;
I+2H=G+H,I=G-H;原式=2(G-H)/I=2