计算:(1/2-1/4+1/6-1/8+.+1/198-1/200)/(1/51+1/52+1/53+.+1/100)

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计算:(1/2-1/4+1/6-1/8+.+1/198-1/200)/(1/51+1/52+1/53+.+1/100)
计算:(1/2-1/4+1/6-1/8+.+1/198-1/200)/(1/51+1/52+1/53+.+1/100)

计算:(1/2-1/4+1/6-1/8+.+1/198-1/200)/(1/51+1/52+1/53+.+1/100)
1/2-1/4+1/6-1/8+.+1/198-1/200
= 1/2(1-1/2+1/3-1/4+...+1/99-1/100)
= 1/2[1+1/2+1/3+...+1/100 - 2*(1/2+1/4+1/6+...+1/100)]
=1/2[1+1/2+1/3+...+1/100 -(1+1/2+1/3+...+1/50)]
=1/2(1/51+1/52+1/53+.+1/100)
所以原式 = 1/2