已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20...根据这些等式求值1/1*2+1/2*3+1/3*4+L+1/2008*20
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![已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20...根据这些等式求值1/1*2+1/2*3+1/3*4+L+1/2008*20](/uploads/image/z/5462469-45-9.jpg?t=%E5%B7%B2%E7%9F%A51-1%2F2%3D1%2F2%2C1%2F2-1%2F3%3D1%2F6%2C1%2F3-1%2F4%3D1%2F12%2C1%2F4-1%2F5%3D1%2F20...%E6%A0%B9%E6%8D%AE%E8%BF%99%E4%BA%9B%E7%AD%89%E5%BC%8F%E6%B1%82%E5%80%BC1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2BL%2B1%2F2008%2A20)
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已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20...根据这些等式求值1/1*2+1/2*3+1/3*4+L+1/2008*20
已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20...根据这些等式求值1/1*2+1/2*3+1/3*4+L+1/2008*20
已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20...根据这些等式求值1/1*2+1/2*3+1/3*4+L+1/2008*20
已知条件就是告诉要裂项:
1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20
2.原式=1-1/2+1/2-1/3+1/3.+1/2008-1/2009
=1-1/2009
=2008/2009
1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20
1-1/2=1/1*2,1/2-1/3=1/2*3,1/3-1/4=1/3*4,1/4-1/5=1/4*5
1/2008-1/2009=1/2008*2009
1/1*2+1/2*3+1/3*4+L+1/2008*2009
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.....+(1/2008-1/2009)
=1-1/2009
=2008/2009