已知(1/3-1/5)*1/2=1/15,(1/5-1-7)*1/2=1/35,(1/7-1/9)*1/2=1/63……
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已知(1/3-1/5)*1/2=1/15,(1/5-1-7)*1/2=1/35,(1/7-1/9)*1/2=1/63……
![](http://img.wesiedu.com/upload/f/a7/fa705759171aec72b3c3cf202b00116a.jpg)
![](http://img.wesiedu.com/upload/f/a7/fa705759171aec72b3c3cf202b00116a.jpg)
![已知(1/3-1/5)*1/2=1/15,(1/5-1-7)*1/2=1/35,(1/7-1/9)*1/2=1/63……](/uploads/image/z/18123185-65-5.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%881%2F3-1%2F5%EF%BC%89%2A1%2F2%EF%BC%9D1%2F15%2C%EF%BC%881%2F5-1-7%EF%BC%89%2A1%2F2%EF%BC%9D1%2F35%2C%EF%BC%881%2F7-1%2F9%EF%BC%89%2A1%2F2%EF%BC%9D1%2F63%E2%80%A6%E2%80%A6)
(1)原式=1/2 (1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)
=1/2×(1/3-1/13)
=1/2×10/39
=5/39
(2) (3²-1²)/1²×3²+(5²-3²)/(3²×5²)+.+(13²-11²)/(11²×13²)
=1-1²/3²+1/3²-1/5²+.+1/11²-1/13²
=1-1/13²
=1-1/169
=168/169
再问: 有乱码,看不懂
再答: (3方-1方)/1方×3方+(5方-3方)/(3方×5方)+。。。。+(13方-11方)/(11方×13方)
=1-1方/3方+1/3方-1/5方+.....+1/11方-1/13方
=1-1/13方
=1-1/169
=168/169
=1/2×(1/3-1/13)
=1/2×10/39
=5/39
(2) (3²-1²)/1²×3²+(5²-3²)/(3²×5²)+.+(13²-11²)/(11²×13²)
=1-1²/3²+1/3²-1/5²+.+1/11²-1/13²
=1-1/13²
=1-1/169
=168/169
再问: 有乱码,看不懂
再答: (3方-1方)/1方×3方+(5方-3方)/(3方×5方)+。。。。+(13方-11方)/(11方×13方)
=1-1方/3方+1/3方-1/5方+.....+1/11方-1/13方
=1-1/13方
=1-1/169
=168/169