1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101=?怎么计算的?
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![1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101=?怎么计算的?](/uploads/image/z/475296-24-6.jpg?t=1%2F3%2B1%2F3%C3%975%EF%BC%8B1%2F5%C3%977%2B1%2F7%C3%979%2B%E2%80%A6%EF%BC%8B1%2F97%C3%9799%EF%BC%8B1%2F99%C3%97101%3D%3F%E6%80%8E%E4%B9%88%E8%AE%A1%E7%AE%97%E7%9A%84%3F)
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101=?怎么计算的?
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101=?怎么计算的?
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101=?怎么计算的?
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101
=1/2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/99-1/101]
=1/2[1-1/3+1/3-1/5+.+1/99-1/101]
=1/2[1-1/101]
=1/2*100/101
=50/101
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101=?
1/3=(1/2)*(1-1/3)
1/(3*5)=(1/2)*(1/3-1/5)
1/(5*7)=(1/2)*(1/5-1/7)
.......
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=(1/2)(1-1/101)
=(1/2)(100/101)
=50/101
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=(1/2)(1-1/101)
=(1/2)(100/101)
=50/101
1
?
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=(1/2)(1-1/101)
=(1/2)(100/101)
=50/101
应该是这样:
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101
=1/2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/99-1/101]
=1/2[1-1/3+1/3-1/5+....+1/99-1/101]
=1/2[1-1/101]
=1/2*100/101
=50/101
不知道对不对!
0
1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101
=1/2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/99-1/101]
=1/2[1-1/3+1/3-1/5+....+1/99-1/101]
=1/2[1-1/101]
=1/2*100/101
=50/101
1365