Question

thu gọn :

a) \(\left(2+1\right)\left(2^2+1\right).....\left(2^{256}+1\right)-1\)

b) \(24\left(5^2+1\right)\left(5^4+1\right)......\left(5^{32}+1\right)-5^{64}\)

Answer 1

a)\(\left(2+1\right)\left(2^2+1\right)....\left(2^{256}+1\right)-1\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)...\left(2^{256}+1\right)-1\)

\(=\left(2^2-1\right)\left(2^2+1\right)...\left(2^{256}+1\right)-1\)

Tiếp tục như thế, ta được:

\(=\left(2^{256}-1\right)\left(2^{256}+1\right)-1=2^{512}-1-1=2^{512}-2\)

b) \(24\left(5^2+1\right)\left(5^4+1\right)...\left(5^{32}+1\right)-5^{64}\)

\(=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)...\left(5^{32}+1\right)-5^{64}\)

\(=\left(5^4-1\right)\left(5^4+1\right)...\left(5^{32}+1\right)-5^{64}\)

Tiếp tục như thế, ta được:

\(=\left(5^{32}-1\right)\left(5^{32}+1\right)-5^{64}=5^{64}-1-5^{64}=-1\)

Answer 2

\(\left(2+1\right).\left(2^2+1\right)....\left(2^{256}+1\right)-1\)

\(\left(2-1\right).\left(2+1\right).\left(2^2+1\right).....\left(2^{256}+1\right)-1\)

\(=\left(2^2-1\right).\left(2^2+1\right)....\left(2^{256}+1\right)-1\)

\(=\left(2^{256}-1\right).\left(2^{256}+1\right)+1=2^{512}+1\)