1\2*5+1\3*5+1\8*11+.+1\20*23 ( )
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![1\2*5+1\3*5+1\8*11+.+1\20*23 ( )](/uploads/image/z/135486-54-6.jpg?t=1%5C2%2A5%2B1%5C3%2A5%2B1%5C8%2A11%2B.%2B1%5C20%2A23+%28+%29)
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1\2*5+1\3*5+1\8*11+.+1\20*23 ( )
1\2*5+1\3*5+1\8*11+.+1\20*23 ( )
1\2*5+1\3*5+1\8*11+.+1\20*23 ( )
1\2*5+1\3*5+1\8*11+.+1\20*23
=1/3*(1/2-1/5+1/5-1/8+1/8-1/11+.+1/20-1/23)
=1/3*(1/2-1/23)
=1/3*21/46
=7/46
1\2*5+1\5*8+1\8*11+......+1\20*23
=1/3(1/2-1/5+1/5-1/8+1/8-1/11+...+1/20-1/23)
=1/3*(1/2-1/23)
=1/3*21/46
=7/46