小明在计算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仿照上式方法计算:(2+1)(2∧2+1)（2∧4+1）（2∧8+1）…（2∧1024+1）-2∧2048的值.

Question

小明在计算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
仿照上式方法计算:(2+1)(2∧2+1)（2∧4+1）（2∧8+1）…（2∧1024+1）-2∧2048的值.

Answer 1

1=2-1
(2+1)(2^2+1)(2^4+1)(2^8+1)…(2^1024+1)-2^2048
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)…(2^1024+1)-2^2048
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)…(2^1024+1)-2^2048
=(2^4-1)(2^4+1)(2^8+1)…(2^1024+1)-2^2048
=……
=2^2048-1-2^2048
=-1