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1/[n(n+1)(n+2)(n+3)(n+4)(n+5)]
=[1/n(n+1)(n+2)(n+3)(n+4)-1/(n+1)(n+2)(n+3)(n+4)(n+5)]/5
3÷1×2×3×4×5×6+3÷2×3×4×5×6×7+....+3÷11×12×13×14×15×16
=3/5×(1/1*2*3*4*5-1/2*3*4*5*6+1/2*3*4*5*6-1/3*4*5*6*7+...+1/11*12*13*14*15-1/12*13*14*15*16)
=3/5×(1/1*2*3*4*5-1/12*13*14*15*16)
=1/200-1/873600
=4367/873600
=[1/n(n+1)(n+2)(n+3)(n+4)-1/(n+1)(n+2)(n+3)(n+4)(n+5)]/5
3÷1×2×3×4×5×6+3÷2×3×4×5×6×7+....+3÷11×12×13×14×15×16
=3/5×(1/1*2*3*4*5-1/2*3*4*5*6+1/2*3*4*5*6-1/3*4*5*6*7+...+1/11*12*13*14*15-1/12*13*14*15*16)
=3/5×(1/1*2*3*4*5-1/12*13*14*15*16)
=1/200-1/873600
=4367/873600
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