Question

求(3+1)(3^2+1)(3^4+1)......(3^32+1)-2分之3的64次方的值

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Answer 1

(3＋1)(3^2＋1)(3^4＋1)......(3^32＋1)
＝1/2×(3－1)(3＋1)(3^2＋1)(3^4＋1)......(3^32＋1)
＝1/2×(3^2－1)(3^2＋1)(3^4＋1)......(3^32＋1)
＝1/2×(3^4－1)(3^4＋1)......(3^32＋1)
＝……
＝1/2(3^32－1)(3^32＋1)
＝1/2(3^64－1)
＝1/2·3^64－1/2
故原式＝1/2·3^64－1/2－1/2·3^64＝－1/2

Answer 2

解答：
(3+1)(3^2+1)(3^4+1)......(3^32+1)-2分之3的64次方
=（1/2)(3-1)(3+1)(3^2+1)(3^4+1)......(3^32+1)-2分之3的64次方
=(1/2)(3^2-1)(3^2+1)(3^4+1)......(3^32+1)-2分之3的64次方
=(1/2)(3^4-1)(3^4+1)......(3^32+1)-2分之3的64次方
=……
=(1/2)(3^64-1)-(1/2)3^64
=-1/2