(1-1/2+1/3-1/4+1/5-1/6+....+1/99-1/100)/(1/102+1/104+1/106+....+1/200=?急
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分子1-1/2+1/3-1/4+1/5-1/6+...+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+1/5+1/6+...+1/99+1/100)-2×(1/2+1/4+1/6+...+1/100)
= (1+1/2+1/3+1/4+1/5+1/6+...+1/99+1/100)-(1+1/2+1/3+...+1/50)
= 1/51+1/52+1/53+...+1/99+1/100.
分母1/102+1/104+1/106+...+1/200
= 1/2×(1/51+1/52+1/53+...+1/100).
因此分子/分母 = 1/(1/2) = 2.
= (1+1/3+1/5+...+1/99)-(1/2+1/4+1/6+...+1/100)
= (1+1/2+1/3+1/4+1/5+1/6+...+1/99+1/100)-2×(1/2+1/4+1/6+...+1/100)
= (1+1/2+1/3+1/4+1/5+1/6+...+1/99+1/100)-(1+1/2+1/3+...+1/50)
= 1/51+1/52+1/53+...+1/99+1/100.
分母1/102+1/104+1/106+...+1/200
= 1/2×(1/51+1/52+1/53+...+1/100).
因此分子/分母 = 1/(1/2) = 2.
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