(1-1/2+1/3-1/4+...+1/99-1/100)/{1+/(1+10)+1/(2+10)+1/(3+103)+...+1/(50+150)

熱心網(wǎng)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.

熱心網(wǎng)友

1-1/2+1/3-1/4+...+1/99-1/100=1+1/3+1/5+...+1/99-1/2-1/4-1/6-...-1/100=(1+1/2+1/3+1/4+...+1/99+1/100)-2(1/2+1/4+1/6+...+1/100)=(1+1/2+1/3+1/4+...+1/99+1/100)-(1+1/2+1/3+1/4+...+1/50)=1/51+1/52+1/53+...+1/99+1/100原式=(1/51+1/52+1/53+...+1/99+1/100)/[1/(1+101)+1/(2+102)+...+1/(50+150) =(1/51=1/52+1/53+...+1/99+1/100)/[1/2(1/51+1/52+1/53+...+1/100) =2

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