\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{10}+1\right)+1\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)...\left(2^{20}+1\right)+1\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{20}+1\right)+1\)
\(=2^{40}-1+1=2^{40}\)