作业帮求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)……(20^4+1/4)]求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)(20^4+1/4)]
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/24 03:24:38
![求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)……(20^4+1/4)]求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)(20^4+1/4)]](/uploads/image/z/200609-17-9.jpg?t=%E6%B1%82%5B%281%5E4%2B1%2F4%29%283%5E4%2B1%2F4%29%285%5E4%2B1%2F4%29%E2%80%A6%E2%80%A6%2819%5E4%2B1%2F4%29%5D%2F%5B%282%5E4%2B1%2F4%29%284%5E4%2B1%2F4%29%286%5E4%2B1%2F4%29%E2%80%A6%E2%80%A6%2820%5E4%2B1%2F4%29%5D%E6%B1%82%5B%281%5E4%2B1%2F4%29%283%5E4%2B1%2F4%29%285%5E4%2B1%2F4%29%E2%80%A6%E2%80%A6%2819%5E4%2B1%2F4%29%5D%2F%5B%282%5E4%2B1%2F4%29%284%5E4%2B1%2F4%29%286%5E4%2B1%2F4%29%2820%5E4%2B1%2F4%29%5D)
求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)……(20^4+1/4)]求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)(20^4+1/4)]
求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)……(20^4+1/4)]
求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)(20^4+1/4)]
求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)……(20^4+1/4)]求[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)(20^4+1/4)]
a^4+1/4=(a²+1/2)²-a²=(a²+a+1/2)(a²-a+1/2)=[a(a+1)+1/2][a(a-1)+1/2]
所以
[(1^4+1/4)(3^4+1/4)(5^4+1/4)……(19^4+1/4)]/[(2^4+1/4)(4^4+1/4)(6^4+1/4)……(20^4+1/4)]
=[(1*2+1/2)*(1*0+1/2)]·[(3*4+1/2)*(3*2+1/2)]·…·[(19*20+1/2)*(19*18+1/2)]/·[(2*3+1/2)*(2*1+1/2)]·[(4*5+1/2)*(4*3+1/2)]·…·[(20*21+1/2)*(20*19+1/2)]=（1*0+1/2）/（20*21+1/2)=1/841
42
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