乘积(1+2)(1+2^2)(1+2^4)……(1+2^16)+1的值为A:2^32-1B:2^32C:2^16+1D:2^64
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![乘积(1+2)(1+2^2)(1+2^4)……(1+2^16)+1的值为A:2^32-1B:2^32C:2^16+1D:2^64](/uploads/image/z/13935742-70-2.jpg?t=%E4%B9%98%E7%A7%AF%281%2B2%29%281%2B2%5E2%29%281%2B2%5E4%29%E2%80%A6%E2%80%A6%281%2B2%5E16%29%2B1%E7%9A%84%E5%80%BC%E4%B8%BAA%3A2%5E32-1B%3A2%5E32C%3A2%5E16%2B1D%3A2%5E64)
乘积(1+2)(1+2^2)(1+2^4)……(1+2^16)+1的值为A:2^32-1B:2^32C:2^16+1D:2^64
乘积(1+2)(1+2^2)(1+2^4)……(1+2^16)+1的值为
A:2^32-1
B:2^32
C:2^16+1
D:2^64
乘积(1+2)(1+2^2)(1+2^4)……(1+2^16)+1的值为A:2^32-1B:2^32C:2^16+1D:2^64
(1+2)(1+2^2)(1+2^4)……(1+2^16)+1
=(1-2)(1+2)(1+2^2)(1+2^4)……(1+2^16)/(-1)+1
=(1-2^2)(1+2^2)(1+2^4)……(1+2^16)/(-1)+1
=...
=(1-2^16)(1+2^16)/(-1)+1
=2^32-1+1
=2^32
B
(1+2)(1+2^2)(1+2^4)……(1+2^16) 乘 (1-2)
(1-2)(1+2)(1+2^2)(1+2^4)……(1+2^16)
= (1 - 2^2)(1+2^2)(1+2^4)……(1+2^16)
= (1 - 2^4)(1+2^4) …… (1 + 2^16)
……
= 1 - 2^32
所以
(1+2)(1+2^2)(1+2^4)……(1+2^16) = 2^32 -1
原式 = 2^32
答案为 B
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B
B,(1+2)(1+2^2)(1+2^4)……(1+2^16)+乘以-1(1-2)再除以-1
(1-2)(1+2)(1+2^2)(1+2^4)……(1+2^16)+1
=-(1-2^2)(1+2^2)(1+2^4)……(1+2^16)+1
=...
=-(1-2^32)+1
=2^32