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)的值求(1-1/2+1/3-1/4+……+1/99-1/100)/{1/

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)

=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