因式分解(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)

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因式分解(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)

因式分解(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)
因式分解(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)

因式分解(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)
(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/10)(1+1/10)
=(1/2)*(3/2)*(2/3)*(4/3)*(3/4)*(5/4)*.*(9/10)*(11/10)
=(1/2)*(11/10)
=11/20