Question

Rút gọn biểu thức:

a/ A=100^2-99^2+98^2-97^2+...+2^2-1^2

b/ B=3(2^2+1)(2^4+1)...!2^64+1)+1

Answer 1

\(A=100^2-99^2+98^2-97^2+....+2^2-1^2\)

\(=\left(100-99\right).\left(100+99\right)+\left(98-97\right).\left(98+97\right)+....+\left(2-1\right).\left(2+1\right)\)

\(=1+2+....+97+98+99+100=\frac{100.\left(100+1\right)}{2}=5050\)

\(B=3\left(2^2+1\right)\left(2^4+1\right)....\left(2^{64}+1\right)+1=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(=\left(2^4-1\right)\left(2^4+1\right)......\left(2^{64}+1\right)+1=\left(2^8-1\right).....\left(2^{64}+1\right)+1\)

Tiếp tục rút gọn như vậy,ta đc \(B=\left(2^{64}-1\right)\left(2^{64}+1\right)=2^{128}-1+1=2^{128}\)