数学题(2+1)(2的平方+1)(2的4次方+1)...(2的32次方+1)+1怎么算?
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数学题(2+1)(2的平方+1)(2的4次方+1)...(2的32次方+1)+1怎么算?
数学题(2+1)(2的平方+1)(2的4次方+1)...(2的32次方+1)+1怎么算?
数学题(2+1)(2的平方+1)(2的4次方+1)...(2的32次方+1)+1怎么算?
(2+1)(2^2+1)(2^4+1)(2^8+1).(2^32+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1).(2^32+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1).(2^32+1)
=(2^4-1)(2^4+1)(2^8+1).(2^32+1)+1
=(2^8-1)(2^8+1).(2^32+1)+1
=(2^16-1).(2^32+1)+1
.
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
1楼的解法是对的,不过他头几步后面一个+1给漏掉了
这里用到一个技巧,就是前面那一堆
(2+1)(2^2+1)(2^4+1)(2^8+1).......(2^32+1)
多乘了一个 1 就是
1*(2+1)(2^2+1)(2^4+1)(2^8+1).......(2^32+1)
由于2-1=1
故:
(2-1)*(2+1)(2^2+1)(2...
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1楼的解法是对的,不过他头几步后面一个+1给漏掉了
这里用到一个技巧,就是前面那一堆
(2+1)(2^2+1)(2^4+1)(2^8+1).......(2^32+1)
多乘了一个 1 就是
1*(2+1)(2^2+1)(2^4+1)(2^8+1).......(2^32+1)
由于2-1=1
故:
(2-1)*(2+1)(2^2+1)(2^4+1)(2^8+1).......(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1).......(2^32+1)
=(2^4-1)(2^4+1)(2^8+1).......(2^32+1)+1
=(2^8-1)(2^8+1).......(2^32+1)+1
=(2^16-1).......(2^32+1)+1
.......
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
收起
2^64 吧,应该不会错