Question

(（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))

Answer 1

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
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Answer 2

楼主，这道题，您应该找谈情说案的景博（林峰饰）回答，谢谢！