15分之1加35分之1加63分之1加99分之1加143分之1

1/15+1/35+1/63+1/99+1/143
={[(1/3)-(1/5)]/2}+{[(1/5)-(1/7)]/2}+{[(1/7)-(1/9)]/2}+{[(1/9)-(1/11)]/2}+{[(1/11)-(1/13)]/2}
=[(1/3)-(1/5)+(1/5)-(1/7)+(1/7)-(1/9)+(1/9)-(1/11)+(1/11)-(1/13)]/2
=[(1/3)-(1/13)]/2
=(10/39)/2
=5/39
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