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求解(1/4-1)(1/9-1)(1/16-1)(1/25-1).(1/2500-1)
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求解(1/4-1)(1/9-1)(1/16-1)(1/25-1).(1/2500-1)
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答案和解析
(1/4-1)(1/9-1)(1/16-1)(1/25-1).(1/2500-1)
=(1/2-1)(1/2+1)(1/3-1)(1/3+1)(1/4-1)(1/4+1)(1/5-1)(1/5+1).(1/50-1)(1/50+1)
=(-1/2)(3/2)(-2/3)(4/3)(-3/4)(5/4)(-4/5)(6/5).(-48/49)(50/49)(-49/50)(51/50)
=(-1/2)(-2/3)(-3/4)(-4/5)...(-49/50)×(3/2)(4/3)(5/4)...(51/50)
=1/50×51/2
=51/100
=(1/2-1)(1/2+1)(1/3-1)(1/3+1)(1/4-1)(1/4+1)(1/5-1)(1/5+1).(1/50-1)(1/50+1)
=(-1/2)(3/2)(-2/3)(4/3)(-3/4)(5/4)(-4/5)(6/5).(-48/49)(50/49)(-49/50)(51/50)
=(-1/2)(-2/3)(-3/4)(-4/5)...(-49/50)×(3/2)(4/3)(5/4)...(51/50)
=1/50×51/2
=51/100
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