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已知1-1/2=1/2

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