(1-1/2+1/3-1/4+1/5-...+1/99-1/100)/[1/(1+101)+1/(2+102)+1/(3+103)+...+1/(50+150)]=?

熱心網友

(1-1/2+1/3-1/4+...+1/99-1/100)/[1/(1+101)+1/(2+102)+1/(3+103)+...+1/(50+150)]==(1+1/3+..+1/99-1/2-1/4-...-1/100)/(1/102+1/104+..+1/200)==[1+1/2+..+1/100-2(1/2+1/4+..+1/100)]/[1/2(1/51+..+1/100)]==[1+1/2+..+1/100-(1/1+1/2+..+1/50)]/[1/2(1/51+..+1/100)]==(1/51+..+1/100)/[1/2(1/51+..+1/100)]=2.