4/3*9/8*16/15*25/24*36/35*49/48*64/63*81/80*100/9
4/3*9/8*16/15*25/24*36/35*49/48*64/63*81/80*100/99如何寻找归律...
4/3*9/8*16/15*25/24*36/35*49/48*64/63*81/80*100/99如何寻找归律
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4/3*9/8*16/15*25/24*36/35*49/48*64/63*81/80*100/99
=[2²/(2+1)(2-1)][3²/(3+1)(3-1)][4²/(4+1)(4-1)]......[10²/(10+1)(10-1)]
=(2²3²4²......10²)/[(2+1)(2-1)(3+1)(3-1)(4+1)(4-1)......(10+1)(10-1)]
=(2²3²4²......10²)/[(2-1)(3-1)(4-1)......(10-1)(2+1)(3+1)(4+1)......(10+1)]
=(2²3²4²......10²)/[(1*2*3......*9)*(3*4......*11)]
=(10*2)/11
=20/11
=[2²/(2+1)(2-1)][3²/(3+1)(3-1)][4²/(4+1)(4-1)]......[10²/(10+1)(10-1)]
=(2²3²4²......10²)/[(2+1)(2-1)(3+1)(3-1)(4+1)(4-1)......(10+1)(10-1)]
=(2²3²4²......10²)/[(2-1)(3-1)(4-1)......(10-1)(2+1)(3+1)(4+1)......(10+1)]
=(2²3²4²......10²)/[(1*2*3......*9)*(3*4......*11)]
=(10*2)/11
=20/11
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