Re: [中學] 求一題分數級數和解法

[Honor1984 (希望願望成真)]

※ 引述《artie0906 (Donut's Dad)》之銘言：
: http://i.imgur.com/ZC8vvjG.jpg

q = 1/1 - 1/2 + 1/3 - 1/4 + ... + 1/101 - 1/102

  = [1/1 + 1/2 + ... + 1/102] - 2[1/2 + 1/4 + 1/6 + ... + 1/102]

  = [1/1 + 1/2 + ... + 1/102] - [1/1 + 1/2 + ... + 1/51]

  = 1/52 + 1/53 + ... + 1/102

p = (1/154){[1/52 + 1/102] + [1/53 + 1/101] + ... + [1/102 + 1/52]}

  = (1/77)(1/52 + 1/53 + ... + 1/102)

=> q/p = 77

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