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(1+1/3)(1+1/8)(1+1/15)(1+1/24)...(1+1/143)
题目详情
(1+1/3)(1+1/8)(1+1/15)(1+1/24)...(1+1/143)
▼优质解答
答案和解析
(4/3) * (9/8)*(16/15)*(25/24).(144/143)
=(2*3*4*5*6*7*8*9*10*11*12)的平方 / [(2方-1)(3方-1)(4方-1)...(12方-1)]
=(2*3...12)方/ [ (2+1)(2-1)(3+1)(3-1)(4+1)(4-1)...(12+1)(12-1) ]
=(2*3...12)方/ [ (2-1)(3-1)(2+1)方(3+1)方.(10+1)方 (11+1)(12+1) ]
=(2*3...12)方/ [ (2-1)(3-1)(3)方(4)方.(11)方 (11+1)(12+1) ]
=2方12方/ [ (2-1)(3-1)(11+1)(12+1) ]
=2*12 / [ (2-1)(12+1) ]
=24/13
=(2*3*4*5*6*7*8*9*10*11*12)的平方 / [(2方-1)(3方-1)(4方-1)...(12方-1)]
=(2*3...12)方/ [ (2+1)(2-1)(3+1)(3-1)(4+1)(4-1)...(12+1)(12-1) ]
=(2*3...12)方/ [ (2-1)(3-1)(2+1)方(3+1)方.(10+1)方 (11+1)(12+1) ]
=(2*3...12)方/ [ (2-1)(3-1)(3)方(4)方.(11)方 (11+1)(12+1) ]
=2方12方/ [ (2-1)(3-1)(11+1)(12+1) ]
=2*12 / [ (2-1)(12+1) ]
=24/13
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