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问题: 请详细解释

1/5x9+1/9x13+1/13x17+......+1/101x105=?

解答:

1/5x9+1/9x13+1/13x17+......+1/101x105
=1/4(1/5-1/9)+1/4(1/9-1/13)+1/4(1/13-1/17)+......+1/4(1/101-1/105)
=1/4(1/5-1/105)
=1/21.