(1+2/3)x(1-2/3)x(1+2/5)x(1-2/5)x……x(1+2/99)x(1-2/99) 等于多少?
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(1+2/3)x(1-2/3)x(1+2/5)x(1-2/5)x……x(1+2/99)x(1-2/99) 等于多少?
(1+2/3)x(1-2/3)x(1+2/5)x(1-2/5)x……x(1+2/99)x(1-2/99) 等于多少?
(1+2/3)x(1-2/3)x(1+2/5)x(1-2/5)x……x(1+2/99)x(1-2/99) 等于多少?
原式=5/3x1/3x7/5x3/5x9/7x5/7x-----x101/99x97/99=1/3x101/99=101/297
把原式的个个括号里算出来,发现第一项和第四项,第三项和第六项,第五项和第八项·····两两乘积为1,最后只剩下第二项1/3和倒数第二项101/99.
(1+2/3)x(1-2/3)x(1+2/5)x(1-2/5)x……x(1+2/99)x(1-2/99)
=5/3×1/3×7/5×3/5×......×101/99×97/99
=(5/3×7/5)×(1/3×3/5)×....×101/99×97/99
=7/3×1/5×9/7×5/7×.....×101/99×97/99
=(7/3×9/7)×(1/5×5/...
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(1+2/3)x(1-2/3)x(1+2/5)x(1-2/5)x……x(1+2/99)x(1-2/99)
=5/3×1/3×7/5×3/5×......×101/99×97/99
=(5/3×7/5)×(1/3×3/5)×....×101/99×97/99
=7/3×1/5×9/7×5/7×.....×101/99×97/99
=(7/3×9/7)×(1/5×5/7)×......×101/99×97/99
=9/3×1/7×11/9×7/9×......×101/99×97/99
=(9/3×11/9)×(1/7×7/9)×......×101/99×97/99
=11/3×1/9×13/11×9/11×......×101/99×97/99
=.........
=99/3×1/97×101/99×97/99
=(99/3×101/99)×(1/97×97/99)
=101/3×1/99
=101/297
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