某同学在计算3(4+1)(4^2+1)时,把3写成(4-1)后,得3(4+1)(4^2+1)=(4-1)(4+1)(4^2+1)=(4^2-1)(4^2+1)=4^4-1,请总结上述算式的规律,计算：(1+2)(1+2^2)(1+2^4)……(1+2^32)+1

Question

某同学在计算3(4+1)(4^2+1)时,把3写成(4-1) 后,
得3(4+1)(4^2+1)=(4-1)(4+1)(4^2+1)=(4^2-1)(4^2+1)=4^4-1 ,请总结上述算式的规律,计算：(1+2)(1+2^2)(1+2^4)……(1+2^32)+1

Answer 1

(1+2)(1+2^2)(1+2^4)……(1+2^32)+1
=(2-1)(1+2)(1+2^2)(1+2^4)……(1+2^32)+1
=(2^2-1)(2^2+1)(2^4+1)……(2^32+1)+1
反复用平方差
=2^64-1+1
=2^64